{"id":22,"date":"2022-04-13T06:07:58","date_gmt":"2022-04-13T06:07:58","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=22"},"modified":"2025-11-19T06:55:42","modified_gmt":"2025-11-19T06:55:42","slug":"a-6-cube-roots","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/a-6-cube-roots\/","title":{"rendered":"A.6 Cube roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Cube roots<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.7-Cube-roots.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Introduction to Cube Roots:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Definition:<\/strong> The cube root of a number x is a value y such that y\u00b3 =x In other words, y is the number that, when multiplied by itself three times, gives the original number x.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Symbol:<\/strong> The cube root is denoted by &#8220;<strong><sup>3<\/sup>\u221a<\/strong>&#8220;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For example,<strong><sup>3<\/sup>\u221a<\/strong>27 = 3, because 3\u00d73\u00d73 = 27.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Understanding the Concept:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Cube vs. Square:<\/strong> Unlike square roots, which deal with two identical factors, cube roots involve three identical factors. <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For example, <strong><sup>3<\/sup>\u221a<\/strong>64 = 4, because 4\u00d74\u00d74 = 64.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Cube Root of Perfect Cubes:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>A <strong>perfect cube<\/strong> is a number that can be expressed as the cube of an integer. In other words, a perfect cube is a number n that can be written in the form n = a\u00b3 , where aaa is an integer.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>8<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>27<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>64<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>125<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>216<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>343<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>512<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>729<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong><sup>3<\/sup>\u221a<\/strong>1000<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Calculating Cube Roots:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-68486a7f08fa1779152e032c4c3bacde\" style=\"color:#197c00\"><strong>Using a Calculator:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Basic Operation:<\/strong> Show how to find cube roots using the calculator. Most scientific calculators have a function for cube roots.<\/li>\n\n\n\n<li><strong>Example:<\/strong> To find <strong><sup>3<\/sup>\u221a<\/strong>125 enter 125 and use the cube root function to get 5.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>Manual Calculation:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-d0a3617be1283dfc5a5de536976be9d8\" style=\"color:#7d0037\"><strong>Prime Factorization Method:<\/strong><\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Factor the number into its prime factors.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Group the factors into sets of three.<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Multiply one number from each set to get the cube root.<\/p>\n\n\n\n<p><strong>Example:<\/strong> For <strong><sup>3<\/sup>\u221a<\/strong>216<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factorization: 216 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3<\/li>\n\n\n\n<li>Grouped factors: (2, 2, 2) and (3, 3, 3)<\/li>\n\n\n\n<li>Cube root: 2 \u00d7 3 = 6<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Estimating Cube Roots:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color has-normal-font-size wp-elements-ed7e5636d41d850eba5ce2419ae37add\">Finding the Nearest Perfect Cubes:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Estimate <strong><sup>3<\/sup>\u221a<\/strong>50.<\/li>\n\n\n\n<li>We know that <strong><sup>3<\/sup>\u221a<\/strong>27\u22483 and <strong><sup>3<\/sup>\u221a<\/strong>64 \u22484<\/li>\n\n\n\n<li>Therefore, <strong><sup>3<\/sup>\u221a<\/strong>50 is between 3 and 4, closer to 4.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Applications of Cube Roots:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Geometry:<\/strong> Finding the side length of a cube when the volume is known. If the volume is 64&nbsp;cubic&nbsp;units, the side length is <strong><sup>3<\/sup>\u221a<\/strong>64 = 4 units.<\/li>\n\n\n\n<li><strong>Science:<\/strong> Cube roots can be used in various scientific calculations, such as determining the volume of substances.<\/li>\n\n\n\n<li><strong>Real-World Problems:<\/strong> Cube roots are used in problems involving the dimensions of objects with cubic shapes.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Conclusion and Review:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Summarize the key points about cube roots, including their definition, calculation methods, and applications.<\/li>\n\n\n\n<li>Reinforce the importance of understanding cube roots in solving real-world problems and in advanced math.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Learn with an example<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b7f2cb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the cube root of&nbsp;0?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;0,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;0.<\/p>\n\n\n\n<p>The number 0 cubed equals 0.<\/p>\n\n\n\n<p>0<sup>3<\/sup> = 0 . 0 . 0 = 0<\/p>\n\n\n\n<p>So the cube root of 0 is 0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e4c2f8\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the cube root of&nbsp;1,000?<\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;1,000,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;1,000.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;10&nbsp;cubed equals&nbsp;1,000.<\/p>\n\n\n\n<p>10<sup>3<\/sup> = 10 . 10 . 10 = 1000<\/p>\n\n\n\n<p>So the cube root of 1,000 is 10.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#bee6f4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the cube root of&nbsp;125?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;125,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;125.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;5&nbsp;cubed equals&nbsp;125.<\/p>\n\n\n\n<p>5<sup>3<\/sup> = 5 . 5 . 5 = 125<\/p>\n\n\n\n<p>So the cube root of 125 is 5.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/75714\/331\/304\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3.png\" alt=\"\" class=\"wp-image-7073\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/34142\/032\/139\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2.png\" alt=\"\" class=\"wp-image-7074\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Cube roots key notes : Introduction to Cube Roots: Definition: The cube root of a number x is a value y such that y\u00b3 =x In other words, y is the number that, when multiplied by itself three times, gives the original number x. Symbol: The cube root is denoted by &#8220;3\u221a&#8220; Understanding the Concept:<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/a-6-cube-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.6 Cube roots&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-22","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=22"}],"version-history":[{"count":31,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/22\/revisions"}],"predecessor-version":[{"id":18240,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/22\/revisions\/18240"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}