{"id":130,"date":"2022-04-12T12:11:17","date_gmt":"2022-04-12T12:11:17","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=130"},"modified":"2025-10-14T11:47:11","modified_gmt":"2025-10-14T11:47:11","slug":"f-21-solve-equations-involving-cubes-and-cube-roots","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-21-solve-equations-involving-cubes-and-cube-roots\/","title":{"rendered":"F.21 Solve equations involving cubes and cube roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve equations involving cubes and cube roots<\/strong><\/h2>\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<h3 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-36f9214c5a831e287f7b3f36c17c191d\">\ud83d\udfe2 <strong>Solve Equations Involving Cubes and Cube Roots<\/strong><\/h3>\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>Cube of a Number<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>cube<\/strong> of a number a is a<sup>3<\/sup>=a\u00d7a\u00d7a<\/li>\n\n\n\n<li>Example: 2<sup>3<\/sup>=2\u00d72\u00d72=8<\/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>Cube Root of a Number<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>cube root<\/strong> of a number b is a number x such that x<sup>3<\/sup>=b<\/li>\n\n\n\n<li>Denoted as \u221bb=x<\/li>\n\n\n\n<li>Example: \u221b27=3, because 3<sup>3<\/sup>=27<\/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>Solving Equations Using Cubes<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>General form: x<sup>3<\/sup>=k<\/li>\n\n\n\n<li>To solve: Take <strong>cube root<\/strong> on both sides:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">x=\u221bk\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: x<sup>3<\/sup>=64<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">x=\u221b64=4<\/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><strong>Solving Equations Using Cube Roots<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>General form: \u221bx=k<\/li>\n\n\n\n<li>To solve: Cube both sides:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">x=k<sup>3<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: \u221bx=5<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">x=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><strong>Equations with Constants on Both Sides<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Example: x<sup>3<\/sup>+8=27<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Subtract 8 from both sides: x<sup>3<\/sup> = 19<\/li>\n\n\n\n<li>Take cube root: x = \u221b19<\/li>\n<\/ol>\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>Negative Numbers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cubes of negative numbers are negative:<br>(\u22122)<sup>3<\/sup>=\u22128<\/li>\n\n\n\n<li>Cube roots of negative numbers are negative:<br>\u221b\u221227=\u22123<\/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>Tips &amp; Tricks<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Only <strong>one real solution<\/strong> exists for cube and cube root equations.<\/li>\n\n\n\n<li>Always <strong>isolate the cube or cube root<\/strong> first before solving.<\/li>\n\n\n\n<li>Check your answer by <strong>cubing<\/strong> or <strong>taking cube root<\/strong> to verify.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <strong>Quick Reminder:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u221bx<sup>3<\/sup> = x and (\u221bx)<sup>3<\/sup> = x<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/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-96ebfd080386f52790815357baf9af50\" style=\"background-color:#eff4b4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-primary-color has-text-color\">Look&nbsp;at this&nbsp;equation:<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color\">a<sup>3<\/sup> =125<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What&nbsp;is&nbsp;a,&nbsp;the cube root of&nbsp;125?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color\">a=___<\/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>In&nbsp;other words, the equation&nbsp;a<sup>3<\/sup> =125&nbsp;is true when&nbsp;a=5.<\/p>\n\n\n\n<p>So&nbsp;the cube root of&nbsp;125&nbsp;is&nbsp;5.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b7f6f9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-primary-color has-text-color\">Look&nbsp;at this&nbsp;equation:<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color\">t<sup>3<\/sup> =8<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What&nbsp;is&nbsp;t,&nbsp;the cube root of&nbsp;8?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color\">t=____<\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;8,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;8.<\/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>In&nbsp;other words, the equation&nbsp;t<sup>3<\/sup> =8&nbsp;is true when&nbsp;t=2.<\/p>\n\n\n\n<p>So&nbsp;the cube root of&nbsp;8&nbsp;is&nbsp;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-358bce49182a1be91e3ad77ccd6ecc71\" style=\"background-color:#9c9cf4\"><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>Look&nbsp;at this&nbsp;equation:<\/p>\n\n\n\n<p>s<sup>3<\/sup> = 27<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f4011586941a942745edcfb6fe65de25\" style=\"color:#b00012\"><strong>What&nbsp;is&nbsp;s,&nbsp;the cube root of&nbsp;27?<\/strong><\/p>\n\n\n\n<p>s=<\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the cube root of&nbsp;27,&nbsp;so figure out which number cubed (multiplied by itself, and then multiplied by itself again) equals&nbsp;27.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;3&nbsp;cubed equals&nbsp;27.<\/p>\n\n\n\n<p>3<sup>3<\/sup>=3.3.3=27<\/p>\n\n\n\n<p>In&nbsp;other words, the equation 3<sup>3<\/sup>=27 is true when s=3.<\/p>\n\n\n\n<p>So&nbsp;the cube root of&nbsp;27&nbsp;is&nbsp;3.<\/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\/78261\/891\/676\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-305.png\" alt=\"\" class=\"wp-image-9614\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-305.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-305-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-305-150x150.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\/976\/509\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-312.png\" alt=\"\" class=\"wp-image-9615\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-312.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-312-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-312-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve equations involving cubes and cube roots Key Notes : \ud83d\udfe2 Solve Equations Involving Cubes and Cube Roots Cube of a Number Cube Root of a Number Solving Equations Using Cubes x=\u221bk\u200b x=\u221b64=4 Solving Equations Using Cube Roots x=k3 x=53=125 Equations with Constants on Both Sides Example: x3+8=27 Negative Numbers Tips &amp; Tricks \ud83d\udca1 Quick<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-21-solve-equations-involving-cubes-and-cube-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.21 Solve equations involving cubes and 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-130","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\/130","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=130"}],"version-history":[{"count":36,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/130\/revisions"}],"predecessor-version":[{"id":21902,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/130\/revisions\/21902"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}