{"id":116,"date":"2022-04-12T12:09:12","date_gmt":"2022-04-12T12:09:12","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=116"},"modified":"2025-10-29T10:14:05","modified_gmt":"2025-10-29T10:14:05","slug":"f-14-square-roots-of-perfect-squares","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-14-square-roots-of-perfect-squares\/","title":{"rendered":"F.14 Square roots of perfect squares"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Square roots of perfect squares<\/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 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 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\/DAG3Kvzoed4\/ACGARDYldPwCh9J9BKoBbw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3Kvzoed4&#x2F;ACGARDYldPwCh9J9BKoBbw&#x2F;watch?utm_content=DAG3Kvzoed4&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<\/div>\n<\/div>\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<h2 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-05099098a4124d1cdd5a225eb2371ba9\">\ud83d\udfe9<strong> Square Roots of Perfect Squares<\/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\udca1 <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, when <strong>multiplied by itself<\/strong>, gives the original number.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a25 = 5 because <strong>5 \u00d7 5 = 25<\/strong> \u2705<\/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>\ud83e\uddee <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 <strong>square of a whole number<\/strong>.<\/p>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1, 4, 9, 16, 25, 36, 49, 64, 81, 100 \u2026<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Number<\/th><th>Perfect Square of<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td>1\u00b2<\/td><\/tr><tr><td>4<\/td><td>2\u00b2<\/td><\/tr><tr><td>9<\/td><td>3\u00b2<\/td><\/tr><tr><td>16<\/td><td>4\u00b2<\/td><\/tr><tr><td>25<\/td><td>5\u00b2<\/td><\/tr><tr><td>36<\/td><td>6\u00b2<\/td><\/tr><tr><td>49<\/td><td>7\u00b2<\/td><\/tr><tr><td>64<\/td><td>8\u00b2<\/td><\/tr><tr><td>81<\/td><td>9\u00b2<\/td><\/tr><tr><td>100<\/td><td>10\u00b2<\/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\udde9 <strong>Symbol of Square Root<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The symbol <strong>\u221a<\/strong> is called the <strong>radical sign<\/strong>.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a49 = 7 \u2728<\/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>\ud83e\udde0 <strong>Finding Square Roots of Perfect Squares<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>There are <strong>three methods<\/strong> to find square roots:<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>\ud83d\udd39 (a) Prime Factorization Method<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Express the number as a product of <strong>prime factors<\/strong>.<\/li>\n\n\n\n<li>Make pairs of the same factors.<\/li>\n\n\n\n<li>Take one factor from each pair and multiply them.<\/li>\n<\/ul>\n\n\n\n<p><strong>\ud83d\udc49 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a144<\/li>\n\n\n\n<li>= \u221a(2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3)<\/li>\n\n\n\n<li>= 2 \u00d7 2 \u00d7 3 = <strong>12<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>\ud83d\udd39 (b) Repeated Subtraction Method<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtract <strong>consecutive odd numbers<\/strong> starting from 1 until you reach 0.<\/li>\n\n\n\n<li>The <strong>number of subtractions<\/strong> gives the square root.<\/li>\n<\/ul>\n\n\n\n<p><strong>\ud83d\udc49 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>49 \u2212 1 = 48<\/li>\n\n\n\n<li>48 \u2212 3 = 45<\/li>\n\n\n\n<li>45 \u2212 5 = 40<\/li>\n\n\n\n<li>40 \u2212 7 = 33<\/li>\n\n\n\n<li>33 \u2212 9 = 24<\/li>\n\n\n\n<li>24 \u2212 11 = 13<\/li>\n\n\n\n<li>13 \u2212 13 = 0<\/li>\n<\/ul>\n\n\n\n<p>\u2714 There are <strong>7 subtractions<\/strong>, so \u221a49 = <strong>7<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>\ud83d\udd39 (c) Estimation Method<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Used when the number is <strong>not a perfect square<\/strong>.<\/li>\n\n\n\n<li>Find the <strong>nearest perfect squares<\/strong> and estimate the root.<\/li>\n\n\n\n<li>\ud83d\udc49 <strong>Example<\/strong>: \u221a50 is between \u221a49 (=7) and \u221a64 (=8).<br>So \u221a50 \u2248 7.1<\/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\udfe6 <strong>Properties of Square Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>1\ufe0f\u20e3 \u221a(a \u00d7 b) = \u221aa \u00d7 \u221ab<\/p>\n\n\n\n<p>2\ufe0f\u20e3 \u221a(a\/b) = \u221aa \u00f7 \u221ab<\/p>\n\n\n\n<p>3\ufe0f\u20e3 (\u221aa)\u00b2 = a<\/p>\n\n\n\n<p>4\ufe0f\u20e3 \u221a(a\u00b2) = |a| (always positive)<\/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>\ud83c\udfaf <strong>Square Root of Zero and One<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a0 = 0<\/li>\n\n\n\n<li>\u221a1 = 1<\/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>\u26a1 <strong>Fun Fact<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The square root of a <strong>perfect square<\/strong> is <strong>always a whole number<\/strong>, but the square root of a <strong>non-perfect square<\/strong> is <strong>irrational<\/strong>.<\/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>\ud83c\udf08 <strong>Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Expression<\/th><th>Solution<\/th><th>Answer<\/th><\/tr><\/thead><tbody><tr><td>\u221a16<\/td><td>4 \u00d7 4 = 16<\/td><td>4<\/td><\/tr><tr><td>\u221a121<\/td><td>11 \u00d7 11 = 121<\/td><td>11<\/td><\/tr><tr><td>\u221a225<\/td><td>15 \u00d7 15 = 225<\/td><td>15<\/td><\/tr><tr><td>\u221a400<\/td><td>20 \u00d7 20 = 400<\/td><td>20<\/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\udcac <strong>Remember<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 The square root \u201cundoes\u201d squaring.<\/p>\n\n\n\n<p>\ud83d\udc49 Perfect squares have <strong>exact<\/strong> square roots.<\/p>\n\n\n\n<p>\ud83d\udc49 Non-perfect squares give <strong>decimal or irrational<\/strong> results.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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-d9e5c8846acdd19a9b793565e7f9fa5a\" style=\"background-color:#e7c3c3\"><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-text-color has-background has-link-color wp-elements-60b7b684917426dfbeeae2c788eb6067\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>What&nbsp;is&nbsp;\u221a81?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You want to find the positive square root of 81 <\/p>\n\n\n\n<p>Figure out which number squared (multiplied by itself) equals 81 .<\/p>\n\n\n\n<p>The number 9 squared equals 81 .<\/p>\n\n\n\n<p>9<sup>2<\/sup>=9.9=81<\/p>\n\n\n\n<p>So \u221a81 is 9<\/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-fc5a609bdfd7fb3a76748b7f5ab86456\" style=\"background-color:#90d4f7\"><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-54504a8097ccc58c0cd82a2943c899c5\" style=\"color:#b00012\"><strong>What&nbsp;is&nbsp;\u221a9?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You want to find the positive square root of 9.<\/p>\n\n\n\n<p>Figure out which number squared (multiplied by itself) equals 9.<\/p>\n\n\n\n<p>The number3 squared equals 9 .<\/p>\n\n\n\n<p>3<sup>2<\/sup> =3.3 = 9<\/p>\n\n\n\n<p>So  \u221a9 is 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-a2dc1342a34eaf6ce427e150c8991c2c\" style=\"background-color:#8ed98e\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-tertiary-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-283a6d38fe57393e505a44db16e9131f\" style=\"color:#b00012\"><strong>What&nbsp;is&nbsp;\u221a100 ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You want to find the positive square root of 100.<\/p>\n\n\n\n<p>Figure out which number squared (multiplied by itself) equals 100.<\/p>\n\n\n\n<p>The number10 squared equals 100 .<\/p>\n\n\n\n<p>10<sup>2<\/sup> = 10 . 10 = 100<\/p>\n\n\n\n<p>So \u221a100 is 10.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s try some problems!\u270d\ufe0f<\/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\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/37616\/227\/735\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-298.png\" alt=\"\" class=\"wp-image-9587\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-298.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-298-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-298-150x150.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\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/33894\/396\/139\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-305.png\" alt=\"\" class=\"wp-image-9588\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-305.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-305-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-305-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Square roots of perfect squares Design by Delta publications Key Notes : \ud83d\udfe9 Square Roots of Perfect Squares \ud83d\udca1 What is a Square Root? The square root of a number is the value that, when multiplied by itself, gives the original number. Example: \ud83e\uddee Perfect Squares A perfect square is a number that is the<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-14-square-roots-of-perfect-squares\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.14 Square roots of perfect squares&#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-116","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\/116","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=116"}],"version-history":[{"count":27,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/116\/revisions"}],"predecessor-version":[{"id":22057,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/116\/revisions\/22057"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}