{"id":153914,"date":"2022-03-25T22:57:10","date_gmt":"2022-03-25T17:27:10","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/cube-root-definition-symbol-properties-and-cube-roots-of-numbers\/"},"modified":"2024-08-29T15:41:52","modified_gmt":"2024-08-29T10:11:52","slug":"cube-root-definition-symbol-properties-and-cube-roots-of-numbers","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/","title":{"rendered":"Cube Root \u2013 Definition, Properties and Cube Roots of Numbers"},"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\/maths\/cube-root\/#What_is_Cube_Root\" title=\"What is Cube Root?\">What is Cube Root?<\/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\/maths\/cube-root\/#How_to_Use_Cube_Root\" title=\"How to Use Cube Root?\">How to Use Cube 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\/maths\/cube-root\/#What_Are_Perfect_Cubes\" title=\"What Are Perfect Cubes?\">What Are Perfect Cubes?<\/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\/maths\/cube-root\/#How_to_Find_the_Cube_Root_of_a_Number\" title=\"How to Find the Cube Root of a Number?\">How to Find the Cube Root of a Number?<\/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\/maths\/cube-root\/#Cube_Root_Formula\" title=\"Cube Root Formula\">Cube Root Formula<\/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\/maths\/cube-root\/#Cube_of_Negative_Numbers\" title=\"Cube of Negative Numbers\">Cube of Negative Numbers<\/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\/maths\/cube-root\/#Solved_Examples_of_Cube_Root\" title=\"Solved Examples of Cube Root\">Solved Examples of Cube Root<\/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\/maths\/cube-root\/#Practice_Questions_of_Cube_Root\" title=\"Practice Questions of Cube Root\">Practice Questions of Cube Root<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/#Cube_Root_FAQs\" title=\"Cube Root: FAQs\">Cube Root: FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/#What_is_a_cube_root\" title=\"What is a cube root?\">What is a cube root?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/#How_do_you_calculate_the_cube_of_a_fraction\" title=\"How do you calculate the cube of a fraction?\">How do you calculate the cube of a fraction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/#What_happens_when_you_cube_a_negative_number\" title=\"What happens when you cube a negative number?\">What happens when you cube a negative number?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>The Cube Root of a number is a special value that, when multiplied by itself three times, gives you the original number. In simple terms, if you take a number and multiply it by itself two more times, the result is known as the cube of that number. This cube is represented as x3, which is read as &#8220;x cubed&#8221; or &#8220;x raised to the power of 3.&#8221;<\/p>\n<p>For example, let\u2019s consider the number 5. When you multiply 5 by itself three times (5 \u00d7 5 \u00d7 5), you get 125. Here, 125 is referred to as the cube of 5 and 5 is the cube root of 125.<\/p>\n<p>Read this article to understand Cube Root in a better way.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root\/\">Cube root<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Cube_Root\"><\/span>What is Cube Root?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The cube root of a number is the value that gives you the original number when cubbed. It\u2019s represented by the symbol 3. Using our earlier example, the cube root of 125 is 5, because<\/p>\n<p>5 \u00d7 5 \u00d7 5 = 125. it is also written as \u221b125 = 5.<\/p>\n<p>If we denote the cube root of a number x as y, the relationship can be expressed with the formula: \u221bx = y<\/p>\n<p>Here, the symbol \u221b represents the cube root, with a small 3 placed in the top left corner to indicate that it is a cube root specifically. Another way to represent the cube root is by using an exponent of 1\/3. For example, x13  also denotes the cube root of x.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Use_Cube_Root\"><\/span>How to Use Cube Root?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The cube root of a number is represented by the symbol \u221b. This symbol is used to denote the value that, when multiplied by itself three times, results in the original number. For example, to express the cube root of 27, we write:<\/p>\n<p>27 = 3 3 3<\/p>\n<p>This means that 3 is the number which, when multiplied by itself three times (3 \u00d7 3 \u00d7 3), gives us 27.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-a-circle\/\">Area of a Circle<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_Are_Perfect_Cubes\"><\/span>What Are Perfect Cubes?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A perfect cube is an integer that can be written as the product of three identical integers. In simpler words, a number is a perfect cube if its cube root is an integer. For an example, 125 is a perfect cube because:<\/p>\n<p>53 = 5 5 5 = 125<\/p>\n<p>On the other hand, 121 is not a perfect cube, as there is no integer that can be multiplied by itself three times to result in 121.<\/p>\n<table>\n<tbody>\n<tr>\n<td>Number<\/td>\n<td>Cube<\/td>\n<td>Number<\/td>\n<td>Cube<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>6<\/td>\n<td>216<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>8<\/td>\n<td>7<\/td>\n<td>343<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>27<\/td>\n<td>8<\/td>\n<td>512<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>64<\/td>\n<td>9<\/td>\n<td>729<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>125<\/td>\n<td>10<\/td>\n<td>1000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/faces-edges-and-vertices\/\"> Vertices, Faces and Edges<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Find_the_Cube_Root_of_a_Number\"><\/span>How to Find the Cube Root of a Number?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Finding the cube root of a number is an easy process when using the prime factorization method. Follow the below-given steps to find the cube root.<\/p>\n<p><b>Step 1:<\/b> Begin with the prime factorization of the given number. Write the prime factors of the number.<\/p>\n<p><b>Step 2:<\/b> Group the prime factors into sets of three identical factors.<\/p>\n<p><b>Step 3:<\/b> Once grouped, remove the cube root symbol and multiply the factors within each group to get the answer. If a factor remains that cannot be grouped into threes, the original number is not a perfect cube, and its cube root cannot be found using this method.<\/p>\n<p>Example: Finding the Cube Root of 15,625<\/p>\n<table style=\"width: 18%;\">\n<tbody>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">15625<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">3125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">625<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">125<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">25<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\">5<\/td>\n<td style=\"width: 51.0288%;\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 45.679%;\"><\/td>\n<td style=\"width: 51.0288%;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>15625 = 56 = 356 = 52 = 25<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube\/\">CUBE<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cube_Root_Formula\"><\/span>Cube Root Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The cube root formula allows us to calculate the cube root of any given number, typically expressed as:<\/p>\n<p>\u221bx = 3 y y y = y<\/p>\n<p>In this formula, y represents the cube root of the number x. This also implies that x is a perfect cube if y is an integer.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cube_of_Negative_Numbers\"><\/span>Cube of Negative Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The process for finding the cube of a negative number is the same as for a positive number or a fraction. The key difference is that the cube of a negative number will always be negative. This is because multiplying three negative numbers together results in a negative product.<\/p>\n<p>For Example: <b>Finding the Cube of -7<\/b><\/p>\n<p>To calculate the cube of -7:<\/p>\n<p>(-7) (-7) (-7) = 49 (-7) = -343<\/p>\n<p>Therefore, the cube of -7 is -343.<\/p>\n<p>Also, <b>Cube Root of -343 is -7. <\/b><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/average\/\">Average<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples_of_Cube_Root\"><\/span>Solved Examples of Cube Root<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li><b> 1. Find the cube of 6.<\/b><\/li>\n<\/ol>\n<p><b>Ans.<\/b> To find the cube of 6, multiply 6 by itself three times:<\/p>\n<p>6 \u00d7 6 \u00d7 6 = 36 \u00d7 6 = 216<\/p>\n<p>Answer: The cube of 6 is 216.<\/p>\n<ol start=\"2\">\n<li><b> 2. Find the cube root of 512.<\/b><\/li>\n<\/ol>\n<p><b>Ans. <\/b>Since 512 is a perfect cube, we can express it as:<\/p>\n<p>512=(2 \u00d7 2 \u00d7 2) \u00d7 (2 \u00d7 2 \u00d7 2) \u00d7 (2 \u00d7 2 \u00d7 2)=2 \u00d7 2 \u00d7 2 = 8<\/p>\n<p>Answer: The cube root of 512 is 8.<\/p>\n<ol start=\"3\">\n<li><b> 3. Find the cube of <\/b><b>3<\/b><b>2<\/b><b>.<\/b><\/li>\n<\/ol>\n<p><b>Ans.<\/b> To find the cube of <b>3<\/b><b>2<\/b>, multiply <b>3<\/b><b>2<\/b> by itself three times:<\/p>\n<p>32 \u00d7 32 \u00d7 32 = 278<\/p>\n<p>Answer: The cube of <b>3<\/b><b>2<\/b> is <b>27<\/b><b>8<\/b>.<\/p>\n<ol start=\"4\">\n<li><b> 4. Find the cube of -6.<\/b><\/li>\n<\/ol>\n<p><b>Ans.<\/b> To find the cube of -6, multiply -6 by itself three times:<\/p>\n<p>-6 \u00d7 -6 \u00d7 -6 = 36 \u00d7 (- 6) = -216<\/p>\n<p>Answer: The cube of -6 is -216.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Practice_Questions_of_Cube_Root\"><\/span>Practice Questions of Cube Root<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Find the cube of 12.<\/p>\n<p>2. Find the cube root of 27000.<\/p>\n<p>3. Find the cube of 65.<\/p>\n<p>4. Find the cube of -11.<\/p>\n<p>5. Find the cube of 15.<\/p>\n<p>6. Find the cube root of 729.<\/p>\n<p>7. Find the cube of 59.<\/p>\n<p>8. Find the cube of -4.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cube_Root_FAQs\"><\/span>Cube Root: FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_cube_root\"><\/span>What is a cube root?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe cube root of a number is a value that, when multiplied by itself three times, equals the original number. For example, the cube root of 27 is 3 because 3\u00d73\u00d73=27. It is denoted by the symbol \u221b.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_calculate_the_cube_of_a_fraction\"><\/span>How do you calculate the cube of a fraction?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo find the cube of a fraction, multiply the fraction by itself three times. For example, to find the cube of 2\/3, we multiply it by itself thrice. (2\/3) \u00d7 (2\/3) \u00d7 (2\/3) = 8\/27. Therefore, the cube of the fraction 2\/3 is 8\/27.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_happens_when_you_cube_a_negative_number\"><\/span>What happens when you cube a negative number?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tWhen you cube a negative number, the result is always negative. This is because multiplying three negative numbers together results in a negative product. For example, the cube of -4 is -64.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a cube root?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The cube root of a number is a value that, when multiplied by itself three times, equals the original number. For example, the cube root of 27 is 3 because 3\u00d73\u00d73=27. It is denoted by the symbol \u221b.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you calculate the cube of a fraction?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To find the cube of a fraction, multiply the fraction by itself three times. For example, to find the cube of 2\/3, we multiply it by itself thrice. (2\/3) \u00d7 (2\/3) \u00d7 (2\/3) = 8\/27. Therefore, the cube of the fraction 2\/3 is 8\/27.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What happens when you cube a negative number?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"When you cube a negative number, the result is always negative. This is because multiplying three negative numbers together results in a negative product. For example, the cube of -4 is -64.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>The Cube Root of a number is a special value that, when multiplied by itself three times, gives you the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Cube Root","_yoast_wpseo_title":"Cube Root \u2013 Definition, Symbol, Properties and Cube Roots of Numbers","_yoast_wpseo_metadesc":"Cube Root is a mathematical function which takes a number and finds the cube root of that number only on Infinitylearn.com.","custom_permalink":"maths\/cube-root\/"},"categories":[13],"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>Cube Root \u2013 Definition, Symbol, Properties and Cube Roots 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