{"id":128,"date":"2022-04-12T12:11:00","date_gmt":"2022-04-12T12:11:00","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=128"},"modified":"2025-10-14T11:49:35","modified_gmt":"2025-10-14T11:49:35","slug":"f-20-estimate-cube-roots","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-20-estimate-cube-roots\/","title":{"rendered":"F.20 Estimate cube roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Estimate 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<h2 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-30db6b32d8e92d471816076a25dd69f9\"><strong>\ud83d\udccc Estimate Cube Roots <\/strong><\/h2>\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>Understanding Cube Roots<\/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 x is a number y such that:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">y<sup>3<\/sup>=x<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Symbolically, \u221bx=y.<\/li>\n\n\n\n<li><strong>Example<\/strong>: \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>Perfect Cubes<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Perfect cubes<\/strong> are numbers like 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.<\/li>\n\n\n\n<li>Knowing perfect cubes helps in estimating cube roots.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Cube<\/th><th>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>10<\/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>Steps to Estimate Cube Roots of Non-Perfect Cubes<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>1. Find two nearest perfect cubes<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify a perfect cube just smaller than the number.<\/li>\n\n\n\n<li>Identify a perfect cube just larger than the number.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Use these cubes to estimate<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cube root will lie <strong>between the roots<\/strong> of these two perfect cubes.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. Refine estimate (optional)<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Compare the number with cubes in-between to get a closer approximation.<\/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>Example 1 \u2013 Estimating \u221b50<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Nearest perfect cubes: 27=3<sup>3<\/sup> and 64=4<sup>3<\/sup><\/li>\n\n\n\n<li>So, \u221b50\u200b lies <strong>between 3 and 4<\/strong>.<\/li>\n\n\n\n<li>Check closer: 3.5<sup>3<\/sup>=42.875, 3.6<sup>3<\/sup>=46.656, 3.7<sup>3<\/sup>=50.653<\/li>\n\n\n\n<li>\u2705 Estimate: \u221b50\u200b\u22483.7<\/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>Example 2 \u2013 Estimating \u221b200<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Nearest perfect cubes: 125=5<sup>3<\/sup> and 216=6<sup>3<\/sup><\/li>\n\n\n\n<li>So, \u221b200\u200b lies <strong>between 5 and 6<\/strong>.<\/li>\n\n\n\n<li>Check closer: 5.8<sup>3<\/sup>=195.112, 5.9<sup>3<\/sup>=205.379<\/li>\n\n\n\n<li>\u2705 Estimate: \u221b200 \u2248 5.85<\/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>Quick Tips<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Memorize perfect cubes up to 10<sup>3<\/sup>=1000 \u2705<\/li>\n\n\n\n<li>Use <strong>trial and error<\/strong> with decimals to refine your estimate<\/li>\n\n\n\n<li>Cube roots of numbers <strong>less than 1<\/strong> are between 0 and 1<\/li>\n\n\n\n<li>Use a calculator for <strong>more accurate estimation<\/strong>, if needed<\/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>Practice Questions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Estimate \u221b90<\/li>\n\n\n\n<li>Estimate \u221b15<\/li>\n\n\n\n<li>Estimate \u221b300<\/li>\n\n\n\n<li>Estimate \u221b0.125<\/li>\n<\/ol>\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-bd9bb935e95d8903cf0e3a550a49909e\" style=\"background-color:#f9aeae\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-e4e66c90b0bec2105ec9b3487000e4f6\"><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-0a3a3dda381d30ff7b8ea7203ca18434\" style=\"color:#b00012\"><strong>Which two&nbsp;integers is <sup>3<\/sup>\u221a49 between ?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 and 6<\/li>\n\n\n\n<li>15 and 16<\/li>\n\n\n\n<li>13 and 14<\/li>\n\n\n\n<li>3 and 4<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the perfect cubes that are just below and just above&nbsp;49.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">The&nbsp;perfect cube just below&nbsp;49&nbsp;is&nbsp;27.<\/p>\n\n\n\n<p>3\u221a27 = 3<\/p>\n\n\n\n<p>The perfect cube just above 49 is 64 .<\/p>\n\n\n\n<p>3\u221a64 = 4<\/p>\n\n\n\n<p>3\u221a27 &lt; 3\u221a49 &lt; 3\u221a64 , so  3 &lt;3\u221a49 &lt; 4.<\/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-653b9b1d642fabf04d6ef182c74b3f99\" style=\"background-color:#edb9e9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-a5ac075b495235599295e791e73d2108\"><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-340aa35f6cbe4183a0d360429ac919fb\" style=\"color:#b00012\"><strong>Which two&nbsp;integers is <sup>3<\/sup>\u221a14 between ?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 and 13<\/li>\n\n\n\n<li>2 and 3<\/li>\n\n\n\n<li>6 and 7<\/li>\n\n\n\n<li>1 and 2<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the perfect cubes that are just below and just above&nbsp;14.<\/p>\n\n\n\n<p>The&nbsp;perfect cube just below&nbsp;14&nbsp;is&nbsp;8.<\/p>\n\n\n\n<p>3\u221a8 = 2<\/p>\n\n\n\n<p>The perfect cube just above 14 is 27 .<\/p>\n\n\n\n<p>3\u221a27 = 3<\/p>\n\n\n\n<p>3\u221a8 &lt; 3\u221a14 &lt; 3\u221a27 , so  2 &lt;3\u221a14 &lt; 3.<\/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-5eaf7aa04061c5f93855c943caebb8ae\" style=\"background-color:#b39ef3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-1129ea7592847451de6054b5261b3721\"><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-b00d9c99dae41876c89e5c449fe44c0c\" style=\"color:#b00012\"><strong>Which two&nbsp;integers is <sup>3<\/sup>\u221a122 between ?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-background-background-color has-background\">\n<li>0 and 1<\/li>\n\n\n\n<li>4 and 5<\/li>\n\n\n\n<li>13 and 14<\/li>\n\n\n\n<li>11 and 12<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the perfect cubes that are just below and just above&nbsp;122.<\/p>\n\n\n\n<p>The&nbsp;perfect cube just below&nbsp;122&nbsp;is&nbsp;64.<\/p>\n\n\n\n<p>3\u221a64 = 4<\/p>\n\n\n\n<p>The perfect cube just above 122 is 125 .<\/p>\n\n\n\n<p>3\u221a125 = 5<\/p>\n\n\n\n<p>3\u221a64 &lt; 3\u221a122 &lt; 3\u221a125 , so  4 &lt;3\u221a122 &lt; 5.<\/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\/78260\/592\/922\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-306.png\" alt=\"\" class=\"wp-image-9617\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-306.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-306-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-306-150x150.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\/687\/866\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-313.png\" alt=\"\" class=\"wp-image-9618\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-313.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-313-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-313-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Estimate cube roots Key Notes : \ud83d\udccc Estimate Cube Roots Understanding Cube Roots y3=x Perfect Cubes Cube Cube Root 1 1 8 2 27 3 64 4 125 5 216 6 343 7 512 8 729 9 1000 10 Steps to Estimate Cube Roots of Non-Perfect Cubes 1. Find two nearest perfect cubes: 2. Use<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-20-estimate-cube-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.20 Estimate 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-128","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\/128","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=128"}],"version-history":[{"count":37,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/128\/revisions"}],"predecessor-version":[{"id":21904,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/128\/revisions\/21904"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}