{"id":156274,"date":"2022-03-26T01:34:28","date_gmt":"2022-03-25T20:04:28","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/cube-root-of-2197-ways-to-find-solved-examples-and-faqs\/"},"modified":"2024-05-06T14:08:41","modified_gmt":"2024-05-06T08:38:41","slug":"cube-root-of-2197-ways-to-find-solved-examples-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/cube-root-of-2197\/","title":{"rendered":"Cube Root of 2197"},"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-of-2197\/#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-of-2197\/#How_to_Find_the_Cube_Root_of_2197\" title=\"How to Find the Cube Root of 2197\">How to Find the Cube Root of 2197<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root-of-2197\/#Cube_Root_of_2197_by_Estimation_Method\" title=\"Cube Root of 2197 by Estimation Method\">Cube Root of 2197 by Estimation Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root-of-2197\/#Cube_Root_of_2197_by_Prime_Factorisation_Method\" title=\"Cube Root of 2197 by Prime Factorisation Method\">Cube Root of 2197 by Prime Factorisation Method<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\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 <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube-root-of-2197\/\">cube root<\/a> of a number is the number that, when multiplied by itself three times, equals the original number. For example, the cube root of 8 is 2, because 2 multiplied by itself three times equals 8.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Find_the_Cube_Root_of_2197\"><\/span>How to Find the Cube Root of 2197<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To find the cube root of 2197, divide 2197 by the cube root of 3.<\/p>\n<p>2197 \/ 3 = 732.33<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cube_Root_of_2197_by_Estimation_Method\"><\/span>Cube Root of 2197 by Estimation Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now let us proceed to calculate the value of <sup>3<\/sup>\u221a2197 following these steps:<\/p>\n<p><strong>Step 1:<\/strong><\/p>\n<p>Take the digit present at the unit\u2019s place of 2197.<\/p>\n<p>Unit Place of 2197 has \u2014&gt; 7<\/p>\n<p><strong>Step 2:<\/strong><\/p>\n<p>Check with the cubes table provided above. The cube of which number has 7 at its unit place?<\/p>\n<p>Clearly, 3<sup>3<\/sup> = 27<\/p>\n<p>That means the cubic root of 2197 will have 3 at the unit place.<\/p>\n<p>Say, <sup>3<\/sup>\u221a2197 = ?3<\/p>\n<p><strong>Step 3:<\/strong><\/p>\n<p>So, we have got the unit place digit of the required value.<\/p>\n<p>Now ignore the last 3 digits of 2197, i.e. 197<\/p>\n<p>Taking 2 as a reference number, we can see 2 lies between 1<sup>3<\/sup> and 2<sup>3<\/sup>, i.e., between 1 and 8.<\/p>\n<p>So, we will choose here the lowest number, nearest to 2, which is 1.<\/p>\n<p>Since, 1<sup>3<\/sup> = 1, therefore, we will have 1 as the first digit of the required number.<\/p>\n<p>Hence, <sup>3<\/sup>\u221a2197 = 13<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cube_Root_of_2197_by_Prime_Factorisation_Method\"><\/span>Cube Root of 2197 by Prime Factorisation Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Here, we will use the prime factorisation method to find the prime factors of 2197. After that, we will pair the factors in a group of three to represent them as cubes. Since the cubes of a number cancel the cube root, therefore we will get the required value.<\/p>\n<p>Let us understand step by step:<\/p>\n<p><strong>Step 1: <\/strong>Find the prime factors of 2197<\/p>\n<p>If we try to divide 2197 by any prime number, we will come to know that the smallest prime number which can divide 2197 is 13. Therefore we get;<\/p>\n<p>2197 = 13\u00d713\u00d713<\/p>\n<p><strong>Step 2: <\/strong>Pair the factors in a group of three and write in the form of cubes.<\/p>\n<p>2197 = (13)<sup>1+1+1<\/sup> = (13)<sup>3<\/sup> [By exponent law: a<sup>m<\/sup>xa<sup>n<\/sup> = a<sup>m+n<\/sup>]\n<p><strong>Step 3:<\/strong> Apply cube root to both sides of the above expression.<\/p>\n<p><sup>3<\/sup>\u221a2197 = <sup>3<\/sup>\u221a(13)<sup>3<\/sup><\/p>\n<p>The cube root gets cancelled by the cube of 13.<\/p>\n<p>Hence, <sup>3<\/sup>\u221a2197 =13<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Cube Root? 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