{"id":126,"date":"2022-04-12T12:10:41","date_gmt":"2022-04-12T12:10:41","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=126"},"modified":"2025-10-29T10:42:45","modified_gmt":"2025-10-29T10:42:45","slug":"f-19-cube-roots-of-perfect-cubes","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-19-cube-roots-of-perfect-cubes\/","title":{"rendered":"F.19 Cube roots of perfect cubes"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Cube roots of perfect cubes<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3KqLE3PY\/-nfCV2-QZy3HjxX4gjRPCg\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KqLE3PY&#x2F;-nfCV2-QZy3HjxX4gjRPCg&#x2F;watch?utm_content=DAG3KqLE3PY&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-09eb8d27d0d70f35bd20b1cf47293f11\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<h1 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-251b936a9986a7e6683676656e8e4f0c\"><strong>\ud83d\udcda Cube Roots of Perfect Cubes <\/strong><\/h1>\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>What is a Cube Root?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>cube root<\/strong> of a number is a value that, when <strong>multiplied by itself three times<\/strong>, gives the original number.<\/p>\n\n\n\n<p>Mathematically:<\/p>\n\n\n\n<p class=\"has-text-align-center\">If&nbsp;a<sup>3<\/sup>=b,&nbsp;then&nbsp;\u221bb=a<\/p>\n\n\n\n<p><strong>Example:<\/strong> \u221b27=3 because&nbsp;3\u00d73\u00d73=27<\/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>Perfect Cubes<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>perfect cube<\/strong> is a number that is the cube of an integer.<\/p>\n\n\n\n<p>Examples of perfect cubes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1, 8, 27, 64, 125, 216, 343, 512, 729, 1000<\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>Quick Tip:<\/strong> The cube of n is n<sup>3<\/sup>.<\/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>Finding Cube Roots of Perfect Cubes<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>1. Identify the perfect cube.<\/p>\n\n\n\n<p>2. Determine the number which, when cubed, gives that perfect cube.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>Examples:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u221b64=4 because&nbsp;4<sup>3<\/sup>=64<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u221b125=5 because&nbsp;5<sup>3<\/sup>=125<\/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>Properties of Cube Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Every positive number has <strong>one positive cube root<\/strong>.<\/li>\n\n\n\n<li>Every negative number has <strong>one negative cube root<\/strong>.<\/li>\n\n\n\n<li>Cube roots of perfect cubes are always <strong>integers<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><strong>Example:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u221b\u221227=\u22123 because&nbsp;(\u22123)<sup>3<\/sup>=\u221227<\/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>Shortcut\/Trick to Remember Cube Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Unit digit method<\/strong>: The last digit of a perfect cube tells the last digit of its cube root:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Cube<\/th><th>Last Digit of Cube Root<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>1<\/td><\/tr><tr><td>8<\/td><td>2<\/td><\/tr><tr><td>27<\/td><td>3<\/td><\/tr><tr><td>64<\/td><td>4<\/td><\/tr><tr><td>125<\/td><td>5<\/td><\/tr><tr><td>216<\/td><td>6<\/td><\/tr><tr><td>343<\/td><td>7<\/td><\/tr><tr><td>512<\/td><td>8<\/td><\/tr><tr><td>729<\/td><td>9<\/td><\/tr><tr><td>1000<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\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>Quick Practice<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find: \u221b512\u200b \u2705 Answer: 8<\/li>\n\n\n\n<li>Find: \u221b\u2212343\u200b \u2705 Answer: -7<\/li>\n\n\n\n<li>Find: \u221b1000\u200b \u2705 Answer: 10<\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udca1 <strong>Remember:<\/strong> Cube roots undo cubing. If n<sup>3<\/sup>=x, then  \u221bx=n.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-453b083764306cb5e6f9c146990dc39f\" style=\"background-color:#bbf2a7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-7d345c65a7b8f2ee4679d510da6e1164\" style=\"color:#b00012\"><strong>\ud83d\udd25What&nbsp;is the cube root of&nbsp;1?&#8212;<\/strong><\/p>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;1,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;1.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;1&nbsp;cubed equals&nbsp;1.<\/p>\n\n\n\n<p>1<sup>3<\/sup>=1 . 1 . 1=1<\/p>\n\n\n\n<p>So&nbsp;the cube root of&nbsp;1&nbsp;is&nbsp;1.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-22e1062ef5e74937f159297c8b057dd3\" style=\"background-color:#f7c5c5\"><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 has-link-color wp-elements-7614d57fcdaf2f5d91c070b8564d6391\" style=\"color:#b00012\"><strong>\ud83d\udd25what is \u221b8 ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;2,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;1.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;2&nbsp;cubed equals&nbsp;8.<\/p>\n\n\n\n<p>2<sup>3<\/sup>=2 . 2 . 2=8<\/p>\n\n\n\n<p>so cube root of 8 is 2.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-91f99f85bab315a3b3b1aa084bdfdedf\" style=\"background-color:#e0befb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color wp-elements-d88ba0348253169757f6c8158f04c45d\" style=\"color:#b00012\"><strong>\ud83d\udd25what is \u221b64 <\/strong><\/p>\n\n\n\n<p>You&nbsp;want to find&nbsp;\u221b64 ,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;64.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;3&nbsp;cubed equals&nbsp;64.<\/p>\n\n\n\n<p>4<sup>3<\/sup>=4.4.4=64<\/p>\n\n\n\n<p>so \u221b64 is 4.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/78207\/950\/221\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-307.png\" alt=\"\" class=\"wp-image-9621\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-307.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-307-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-307-150x150.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\/33897\/402\/547\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-314.png\" alt=\"\" class=\"wp-image-9622\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-314.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-314-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-314-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Cube roots of perfect cubes Design by Delta publications Key Notes : \ud83d\udcda Cube Roots of Perfect Cubes What is a Cube Root? The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Mathematically: If&nbsp;a3=b,&nbsp;then&nbsp;\u221bb=a Example: \u221b27=3 because&nbsp;3\u00d73\u00d73=27 Perfect Cubes A perfect cube is a<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-19-cube-roots-of-perfect-cubes\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.19 Cube roots of perfect cubes&#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-126","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/126","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=126"}],"version-history":[{"count":27,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/126\/revisions"}],"predecessor-version":[{"id":22061,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/126\/revisions\/22061"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}