{"id":608373,"date":"2023-06-19T19:10:07","date_gmt":"2023-06-19T13:40:07","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=608373"},"modified":"2024-07-05T13:00:05","modified_gmt":"2024-07-05T07:30:05","slug":"square-root-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/","title":{"rendered":"Square Root Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#Introduction\" title=\"Introduction:\">Introduction:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#What_is_square_root\" title=\"What is square root? \">What is square root? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#How_to_represent_a_square_root\" title=\"How to represent a square root? \">How to represent a square root? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#How_to_find_the_square_root_of_a_number_in_exponential_form\" title=\"How to find the square root of a number in exponential form? \">How to find the square root of a number in exponential form? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#How_to_find_the_square_root_of_a_number_by_prime_factorization\" title=\"How to find the square root of a number by prime factorization? \">How to find the square root of a number by prime factorization? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#How_to_find_the_square_root_of_a_number_by_long_division\" title=\"How to find the square root of a number by long division? \">How to find the square root of a number by long division? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#Solved_Examples_on_Square_Root_Formula\" title=\"Solved Examples on Square Root Formula: \">Solved Examples on Square Root Formula: <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#Frequently_Asked_Questions_on_Square_Root_Formula\" title=\"Frequently Asked Questions on Square Root Formula: \">Frequently Asked Questions on Square Root Formula: <\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The square root is a mathematical operation that involves finding the value which, when multiplied by itself, gives a given number. It is denoted by the symbol \u221a. Square roots are commonly used in various mathematical and scientific calculations, such as solving equations, measuring distances, and determining the sides of geometric shapes. They play a fundamental role in understanding and manipulating numbers in many areas of mathematics and beyond.<\/span><\/p>\n<h2><b><span data-contrast=\"auto\">What is square root?<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is the inverse operation of the square.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For example,<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The square of 4 is 16. Thus, the square root of 16 is 4.<\/span><\/p>\n<h2><b><span data-contrast=\"auto\">How to represent a square root?<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">The square root is represented by the symbol, \u221a , also known as the radical.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The number inside this symbol is called the Radicand or Base.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For example,<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The square root of 16, is written as \u221a16.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">How to find the square root of a number in exponential form?<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">To find the square root of a number in exponential form, keep the base the same and halve <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">the exponent.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">For example,<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">To find \u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4, we keep the base the same, which is 2, and halve the exponent. So, half of 4, <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">which is 2.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So, \u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4 = 2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2 = 4.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Let us verify this.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4 = 16<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u2234 \u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4 = \u221a16<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u2234 \u221a2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4 = 4<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">How to find the square root of a number by prime factorization?<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">Let us understand the following steps of the prime factorization method by finding the <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">square root of 225.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 1: Find the prime factors.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608575\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png\" alt=\"\" width=\"151\" height=\"270\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 2: Make pairs of the same prime factors.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-608591\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193058.png\" alt=\"\" width=\"214\" height=\"88\" \/><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 3: Choose one number from each pair and multiply.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608593\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193124.png\" alt=\"\" width=\"151\" height=\"73\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 4: The result in step 3 is the square root.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608596\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193147.png\" alt=\"\" width=\"256\" height=\"93\" \/><\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">How to find the square root of a number by long division?<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">The long division method is used to find the square root of large numbers usually.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Let us understand the steps in this method by finding the square root of 8281.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 1: Write the division as shown below:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608604\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193251.png\" alt=\"\" width=\"166\" height=\"214\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 2: Mark pairs of digits from the units end.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, the pairs are 81 and 82.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-medium wp-image-608612\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193328-244x300.png\" alt=\"\" width=\"244\" height=\"300\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193328-244x300.png?v=1687183431 244w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193328.png?v=1687183431 256w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 3: Find a perfect square equal to or just lower than the first pair from the left. Write <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">the square root of this number to the left.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, the first pair is 82.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The perfect square lower and closest to 82 is 81.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">9<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> = 81.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So, write the number 9 to the left of 8281.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-medium wp-image-608634\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193441-300x271.png\" alt=\"\" width=\"300\" height=\"271\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193441-300x271.png?v=1687183567 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193441.png?v=1687183567 313w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 4: Multiply above and add below the same number.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Multiply 9 with 9 and write the product, that is 81, below 82.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Add 9 with 9 and write the sum, that is 18, on the left side.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608636\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193502.png\" alt=\"\" width=\"295\" height=\"300\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 5: Draw a box next to the sum. Subtract the product from the number above it.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, draw a box next to 18 and subtract 81 from 82. This gives 1.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608639\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193525.png\" alt=\"\" width=\"292\" height=\"297\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 6: Bring the next pair down.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The next pair is 81. Bring it down and write it next to 1.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608641\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193545.png\" alt=\"\" width=\"301\" height=\"301\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193545.png?v=1687183593 301w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193545-150x150.png?v=1687183593 150w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 7: Draw a box above and below as shown.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, draw a box next to 9 and another box below the box from step 5.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-medium wp-image-608667\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193710-273x300.png\" alt=\"\" width=\"273\" height=\"300\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193710-273x300.png?v=1687183760 273w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193710.png?v=1687183760 279w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 8: Find a number to fill the boxes such that the product on the left gives the result <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">equal to or less than the number on the right. Use trial and error to find the digit in the <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">boxes. The number is the same in all the boxes. <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, we need to find the number, such that the product we get will be less than or equal to <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> 181. <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608674\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-193730.png\" alt=\"\" width=\"190\" height=\"186\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">In this case it is 1, as 181 \u00d7 1 = 181.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 9: Multiply above and add below.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Multiply by 1 and add 1. The product is 181 and the sum is 182.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608683\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-194025.png\" alt=\"\" width=\"259\" height=\"292\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 10: Subtract the product from the number above it.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Subtracting 181 from 181 gives 0.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608686\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-194044.png\" alt=\"\" width=\"256\" height=\"295\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Step 11: Repeat the above process till 0 is obtained and no more pairs are left. Then the <\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">long division stops.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The number on top of the division is the square root.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608696\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-194137.png\" alt=\"\" width=\"280\" height=\"297\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Here, \u221a8281 = 91<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The final sum on the left of the long division is always twice the number on the top.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">In this case, 182 = 2 \u00d7 91.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Solved Examples on Square Root Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><b><span data-contrast=\"auto\">Example 1:<\/span><\/b><span data-contrast=\"auto\"> Find the square root of 11025.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 1: Find the prime factors of 11025.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"alignnone size-full wp-image-608700\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-194157.png\" alt=\"\" width=\"181\" height=\"240\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">\u2234 11025 = 3 x 3 x 5 x 5 x 7 x 7<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 2: Pair the prime factors.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">11025 = <\/span><span data-contrast=\"auto\">3 x 3<\/span><span data-contrast=\"auto\"> x <\/span><span data-contrast=\"auto\">5 x 5<\/span><span data-contrast=\"auto\"> x <\/span><span data-contrast=\"auto\">7 x 7<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 3: Choose one number from each pair and multiply.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">11025 = 3 x 5 x 7 = 105<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 4: The product in step 3 is the square root of 11025.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u221a11025 = 105<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 2: <\/span><\/b><span data-contrast=\"auto\">Find the square root of 144 using prime factorization.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 1: Prime factorize 144.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">144 = 2x2x2x2x3x2<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 2: Take the square root of each prime factor.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u221a<\/span><span data-contrast=\"auto\">2&#215;2<\/span><span data-contrast=\"auto\">x<\/span><span data-contrast=\"auto\">2&#215;2<\/span><span data-contrast=\"auto\">x<\/span><span data-contrast=\"auto\">3&#215;2<\/span><span data-contrast=\"auto\"> = 12<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Step 3: Simplify the expression.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u221a144 = 12<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Therefore, the square root of 144 is 12.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><b><span data-contrast=\"auto\">Frequently Asked Questions on Square Root Formula:<\/span><\/b><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/h2>\n<p><span data-contrast=\"auto\">1: What is a square root?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: A square root is a value that, when multiplied by itself, gives the original number. It is the inverse operation of squaring.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">2: How to find square root using prime factorization?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: To find the square root of a number using prime factorization, follow these steps:<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">Prime factorize the given number by breaking it down into its prime factors.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">Group the prime factors in pairs, each representing the same factor.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">Take one factor from each pair and write them outside the square root sign.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"4\" data-aria-level=\"1\"><span data-contrast=\"auto\">Multiply the factors written outside the square root sign.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"5\" data-aria-level=\"1\"><span data-contrast=\"auto\">If any factor is left unpaired, write it inside the square root sign.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<ol>\n<li data-leveltext=\"%1.\" data-font=\"Calibri\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:0,&quot;335559684&quot;:-1,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769242&quot;:[65533,1],&quot;469777803&quot;:&quot;right&quot;,&quot;469777804&quot;:&quot;%1.&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"6\" data-aria-level=\"1\"><span data-contrast=\"auto\">Simplify the expression if possible.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ol>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">3: Is a square always positive?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, a square is always positive or zero. When you square a number (multiply it by itself), the result is either positive or zero. Negative numbers do not have real square roots, as the square of a real number cannot be negative.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">4: What are the properties of square roots?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Some properties of square roots include: the square root of a product is the product of the square roots, the square root of a quotient is the quotient of the square roots, and the square root of a squared value is the absolute value of the original value.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">5: Can I approximate square roots without using a calculator?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, you can approximate square roots without a calculator using techniques such as prime factorization, estimation, or using known square roots as reference points. These methods provide reasonable approximations of square roots.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">6: What is a \u221a in math?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: In mathematics, the symbol \u221a represents the square root operation. It is used to denote the principal square root of a number. When a number is written as \u221ax, it means finding the value that, when multiplied by itself, gives x. For example, \u221a25 equals 5, as 5 multiplied by itself is 25. The square root symbol (\u221a) is widely used in various mathematical equations and calculations involving roots, exponents, and quadratic functions.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">7: Is there a square root of zero?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, the square root of zero is zero. When you multiply zero by itself, the result is also zero. Therefore, the square root of zero is zero.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">8: Is 25 a perfect square?<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Answer: Yes, 25 is a perfect square. A perfect square is a number that can be expressed as the square of an integer. In the case of 25, it is equal to 5 raised to the power of 2, which is 5<\/span><span data-contrast=\"auto\">2<\/span><span data-contrast=\"auto\"> = 25.<\/span><span data-ccp-props=\"{&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction: The square root is a mathematical operation that involves finding the value which, when multiplied by itself, gives a [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Square Root Formula\u00a0","_yoast_wpseo_title":"Square Root Formula\u00a0with Examples - Infinity learn","_yoast_wpseo_metadesc":"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.","custom_permalink":"formulas\/square-root-formula\/"},"categories":[8438,8536],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Square Root Formula\u00a0with Examples - Infinity learn<\/title>\n<meta name=\"description\" content=\"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Square Root Formula\u00a0with Examples - Infinity learn\" \/>\n<meta property=\"og:description\" content=\"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-19T13:40:07+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-07-05T07:30:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ankit\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Square Root Formula\u00a0with Examples - Infinity learn","description":"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/","og_locale":"en_US","og_type":"article","og_title":"Square Root Formula\u00a0with Examples - Infinity learn","og_description":"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.","og_url":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2023-06-19T13:40:07+00:00","article_modified_time":"2024-07-05T07:30:05+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Ankit","Est. reading time":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png?v=1687183230","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png?v=1687183230","width":151,"height":270},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/","name":"Square Root Formula\u00a0with Examples - Infinity learn","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#primaryimage"},"datePublished":"2023-06-19T13:40:07+00:00","dateModified":"2024-07-05T07:30:05+00:00","description":"Master the square root formula with our simple guide. Learn how to find square roots easily, perfect for students and anyone needing a quick math refresher.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Square Root Formula\u00a0"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d647d4ff3a1111ff8eeccdb6b12651cb"},"headline":"Square Root Formula\u00a0","datePublished":"2023-06-19T13:40:07+00:00","dateModified":"2024-07-05T07:30:05+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#webpage"},"wordCount":1151,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/formulas\/square-root-formula\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-19-191156.png","articleSection":["Formulas","Math Formulas"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d647d4ff3a1111ff8eeccdb6b12651cb","name":"Ankit","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/b1068bdc2711bd9c9f8be3b229f758f6?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/b1068bdc2711bd9c9f8be3b229f758f6?s=96&d=mm&r=g","caption":"Ankit"},"url":"https:\/\/infinitylearn.com\/surge\/author\/ankit\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/608373"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=608373"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/608373\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=608373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=608373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=608373"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=608373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}