{"id":122,"date":"2022-04-12T12:10:07","date_gmt":"2022-04-12T12:10:07","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=122"},"modified":"2025-10-29T10:32:42","modified_gmt":"2025-10-29T10:32:42","slug":"f-17-relationship-between-squares-and-square-roots","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-17-relationship-between-squares-and-square-roots\/","title":{"rendered":"F.17 Relationship between squares and square roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Relationship between squares and square roots<\/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\/DAG3KtkedO0\/EnNxi2JE4O4MlT-xtzFtQQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KtkedO0&#x2F;EnNxi2JE4O4MlT-xtzFtQQ&#x2F;watch?utm_content=DAG3KtkedO0&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-7464115d112791a83a98a59c10102309\" 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-231fec294bb3fed5d044d895ddc1dda1\">\ud83e\uddee<strong> Relationship Between Squares and Square 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>\ud83d\udd39<strong> What is a Square?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>square of a number<\/strong> is the product of the number multiplied by itself.<\/p>\n\n\n\n<p><strong>\ud83d\udc49 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5<sup>2<\/sup>=5\u00d75=25<\/li>\n<\/ul>\n\n\n\n<p><strong>Symbol:<\/strong> n<sup>2<\/sup> (read as \u201cn squared\u201d)<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Number<\/th><th>Square<\/th><\/tr><\/thead><tbody><tr><td>2<\/td><td>4<\/td><\/tr><tr><td>3<\/td><td>9<\/td><\/tr><tr><td>4<\/td><td>16<\/td><\/tr><tr><td>10<\/td><td>100<\/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>\ud83d\udd39 <strong>What is a Square Root?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>square root<\/strong> of a number is the value that gives the original number when multiplied by itself.<\/p>\n\n\n\n<p><strong>\ud83d\udc49 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a25=5 because 5\u00d75=25<\/li>\n<\/ul>\n\n\n\n<p><strong>Symbol:<\/strong>\u221a\u200b (called the <em>radical sign<\/em>)<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Number<\/th><th>Square Root<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>1<\/td><\/tr><tr><td>4<\/td><td>2<\/td><\/tr><tr><td>9<\/td><td>3<\/td><\/tr><tr><td>16<\/td><td>4<\/td><\/tr><tr><td>25<\/td><td>5<\/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>\ud83d\udd39<strong> Relationship Between Squares and Square Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udca1 <strong>Squares and square roots are inverse (opposite) operations.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Operation<\/th><th>Example<\/th><\/tr><\/thead><tbody><tr><td>If you <strong>square<\/strong> a number and then take the <strong>square root<\/strong>, you get the <strong>original number<\/strong>.<\/td><td>\u221a(5<sup>2<\/sup>)=\u221a25=5<\/td><\/tr><tr><td>If you <strong>take the square root<\/strong> first and then <strong>square<\/strong>, you also get the <strong>original number<\/strong>.<\/td><td>(\u221a9)<sup>2<\/sup>=3<sup>2<\/sup>=9<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2705 <strong>In short:<\/strong> \u221aa2=a and(\u221aa)2=a<\/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>\ud83d\udd39 <strong>Perfect Squares<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>perfect square<\/strong> is a number that is the square of a whole number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 <strong>Example<\/strong>: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udfe2 <strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7<sup>2<\/sup>=49 \u2192 49 is a perfect square<\/li>\n\n\n\n<li>8<sup>2<\/sup>=64 \u2192 64 is a perfect square<\/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>\ud83d\udd39 <strong>Important Facts to Remember<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2728 The square of:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>positive number<\/strong> \u279c is <strong>positive<\/strong><\/li>\n\n\n\n<li>A <strong>negative number<\/strong> \u279c is also <strong>positive<\/strong><br>\ud83d\udc49 Example: (\u22125)<sup>2<\/sup>=25<\/li>\n\n\n\n<li>The <strong>square root<\/strong> of a <strong>positive number<\/strong> \u279c has <strong>two values<\/strong>, one positive and one negative.<br>\ud83d\udc49 Example: \u221a25=\u00b15<\/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>\ud83d\udd39 <strong>Geometric Connection \ud83d\udccf<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>area<\/strong> of a <strong>square<\/strong> = side \u00d7 side = side\u00b2<\/li>\n\n\n\n<li>The <strong>side length<\/strong> = \u221a(area)<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 If the area of a square = 49 cm\u00b2<br>Then, side = \u221a49 = 7 cm<\/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>\ud83d\udd39 <strong>Quick Tricks \ud83e\ude84<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2705 Last digits of perfect squares: 0, 1, 4, 5, 6, 9<\/p>\n\n\n\n<p>\u274c A number ending in 2, 3, 7, or 8 <strong>cannot<\/strong> be a perfect square.<\/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>\ud83e\udde1 <strong>Summary Table<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Concept<\/th><th>Example<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td>Square of 6<\/td><td>6<sup>2<\/sup><\/td><td>36<\/td><\/tr><tr><td>Square Root of 36<\/td><td>\u221a36<\/td><td>6<\/td><\/tr><tr><td>Relationship<\/td><td>\u221a6<sup>2<\/sup>=6<\/td><td>Inverse operations<\/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>\ud83e\udde0 <strong>Remember:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u201cSquaring a number makes it bigger (except 0 and 1),<br>Taking the square root brings it back to the original!\u201d \ud83c\udf08<\/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-background has-normal-font-size\" style=\"background-color:#023533\"><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-text-color has-link-color wp-elements-86c5960f3115b8739be5124d63277675\" style=\"color:#b00012\">Simplify:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d4ac2542a7aaa174af995acf39f9d7ac\" style=\"color:#b00012\">\u221a(36)<sup>2<\/sup>&nbsp;=<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-77419ca7699af2d3113f9f40bb00fecb\">Taking the square root of a number is the inverse of squaring it. The two operations cancel each other out.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-9da7315562d4cc9a91f9056f305ea9e4\">So, \u221a(36)<sup>2<\/sup>&nbsp;= 36<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#4a0244\"><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-text-color has-link-color wp-elements-86c5960f3115b8739be5124d63277675\" style=\"color:#b00012\">Simplify:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-eca2aa8e1611a4f03bbb4a7e5e4d7c33\" style=\"color:#b00012\">\u221a(16)<sup>2<\/sup>&nbsp;=<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-77419ca7699af2d3113f9f40bb00fecb\">Taking the square root of a number is the inverse of squaring it. The two operations cancel each other out.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-1523a3b2a9906346b9fdb47fa23626a5\">So, \u221a(16)<sup>2<\/sup>&nbsp;= 16<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#052c62\"><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 has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-bb211c5adc5fe0acfeda0c6f9db6f350\" style=\"color:#b00012\">Simplify:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-99360ee6348bb27d5604483f39e8898d\" style=\"color:#b00012\">\u221a(81)<sup>2<\/sup>&nbsp;=<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-77419ca7699af2d3113f9f40bb00fecb\">Taking the square root of a number is the inverse of squaring it. The two operations cancel each other out.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-cc5db0fa7769e0d152db2cca8c1a1f7e\">So, \u221a(81)<sup>2<\/sup>&nbsp;= 81<\/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\/78204\/633\/259\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-309.png\" alt=\"\" class=\"wp-image-9628\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-309.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-309-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-309-150x150.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\/33896\/736\/591\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-316.png\" alt=\"\" class=\"wp-image-9629\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-316.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-316-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-316-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Relationship between squares and square roots Design by Delta publications Key Notes: \ud83e\uddee Relationship Between Squares and Square Roots \ud83d\udd39 What is a Square? The square of a number is the product of the number multiplied by itself. \ud83d\udc49 Example: Symbol: n2 (read as \u201cn squared\u201d) \u2728 Examples: Number Square 2 4 3 9 4<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-17-relationship-between-squares-and-square-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.17 Relationship between squares and square 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-122","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\/122","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=122"}],"version-history":[{"count":26,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/122\/revisions"}],"predecessor-version":[{"id":22059,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/122\/revisions\/22059"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}