{"id":20,"date":"2022-04-13T06:07:41","date_gmt":"2022-04-13T06:07:41","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=20"},"modified":"2025-11-20T06:37:02","modified_gmt":"2025-11-20T06:37:02","slug":"a-5-square-roots","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/a-5-square-roots\/","title":{"rendered":"A.5 Square roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Square roots<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.6-Square-roots.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/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>Introduction to Square Roots:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Define what a square root is: the number that, when multiplied by itself, gives the original number.<\/li>\n\n\n\n<li>Example: \u221a9 = 3 because 3 \u00d7 3 = 9.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Perfect Squares:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Discuss numbers like 1, 4, 9, 16, etc., which have whole numbers as square roots.<\/li>\n\n\n\n<li>Explore why some numbers have exact square roots (perfect squares) and others don&#8217;t.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>4<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>9<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>16<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>25<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>36<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>49<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>64<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>81<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>100<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>121<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>144<\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>169<\/td><td class=\"has-text-align-center\" data-align=\"center\">13<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>196<\/td><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>225<\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>256<\/td><td class=\"has-text-align-center\" data-align=\"center\">16<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>289<\/td><td class=\"has-text-align-center\" data-align=\"center\">17<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>324<\/td><td class=\"has-text-align-center\" data-align=\"center\">18<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>361<\/td><td class=\"has-text-align-center\" data-align=\"center\">19<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u221a<\/strong>400<\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Estimating Square Roots:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Techniques for estimating square roots without a calculator.<\/li>\n\n\n\n<li>Example: Estimating \u221a30 is between \u221a25 = 5 and \u221a36 = 6.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Calculating Square Roots:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Basic methods for calculating square roots manually or using a calculator.<\/li>\n\n\n\n<li>Step-by-step process and why it&#8217;s useful in mathematics and everyday life.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-22c9afe5b68fc12def18f2014b858860\" style=\"color:#056000\"><strong>Understanding the Process:<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\"><strong>Definition Recap:<\/strong> A square root of a number x is a value y such that y\u00b2 = x. For example, \u221a16=4 because 4\u00b2 = 16.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-3ca32cfa1668011a22f5e99b5a832801\" style=\"color:#056000\"><strong>Using a Calculator:<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Basic Operation:<\/strong> Show students how to use the square root function on a calculator. For instance, entering 25 and pressing the square root button (\u221a) will yield 5.<\/li>\n\n\n\n<li><strong>Practice:<\/strong> Have students practice finding the square roots of various numbers using calculators.<\/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>Manual Methods for Finding Square Roots:<\/strong><\/strong><\/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><strong>Prime Factorization Method:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Step 1:<\/strong> Factor the number into its prime factors.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Step 2:<\/strong> Pair the prime factors.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Step 3:<\/strong> Multiply one number from each pair to get the square root.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example:<\/strong> To find the square root of 36:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factorization: 36 = 2 \u00d7 2 \u00d7 3 \u00d7 3<\/li>\n\n\n\n<li>Pairs: (2,2) and (3,3)<\/li>\n\n\n\n<li>Square root: 2 \u00d7 3 = 6<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\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>Long Division Method:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Step 1:<\/strong> Pair the digits of the number from right to left (e.g., 36 becomes 36, and 144 becomes 1 44).<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Find the largest number whose square is less than or equal to the first pair. Place this number in the quotient.<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Subtract, bring down the next pair of digits, and repeat the process.<\/li>\n\n\n\n<li><strong>Example:<\/strong> For \u221a144:<\/li>\n\n\n\n<li>12 \u00d7 12 = 144, so \u221a144 = 12.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Square Roots in Pythagorean Theorem:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Introduce how square roots relate to the Pythagorean Theorem (a\u00b2 + b\u00b2 = c\u00b2) in right triangles.<\/li>\n\n\n\n<li>Emphasize the importance of understanding square roots in solving problems involving triangle sides.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Conclusion:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Summarize the key points covered.<\/li>\n\n\n\n<li>Encourage students to practice calculating and estimating square roots to strengthen their skills.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e3bcfa\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the positive square root of&nbsp;100?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You&nbsp;want to find the positive square root of&nbsp;100.<\/p>\n\n\n\n<p>Figure&nbsp;out which number squared (multiplied by itself) equals&nbsp;100.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;10&nbsp;squared equals&nbsp;100.<\/p>\n\n\n\n<p>10<sup>2<\/sup> = 10 . 10 = 100<\/p>\n\n\n\n<p>So the positive square root of 100 is 10.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f3f0b2\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the negative square root of&nbsp;25?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Start&nbsp;by finding the positive square root of&nbsp;25.<\/p>\n\n\n\n<p>Figure&nbsp;out which number squared (multiplied by itself) equals&nbsp;25.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;5&nbsp;squared equals&nbsp;25.<\/p>\n\n\n\n<p>5<sup>2<\/sup> = 5 . 5 = 25<\/p>\n\n\n\n<p>So the positive square root of 25 is 5.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Finally, include the negative sign to get the negative square root.<\/p>\n\n\n\n<p>The negative square root of 25 is \u20135.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#dac0f8\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf What&nbsp;is the negative square root of&nbsp;9?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Start&nbsp;by finding the positive square root of&nbsp;9.<\/p>\n\n\n\n<p>Figure&nbsp;out which number squared (multiplied by itself) equals&nbsp;9.<\/p>\n\n\n\n<p>The&nbsp;number&nbsp;3&nbsp;squared equals&nbsp;9.<\/p>\n\n\n\n<p>3<sup>2<\/sup> = 3 . 3 = 9<\/p>\n\n\n\n<p>So&nbsp;the positive square root of&nbsp;9&nbsp;is&nbsp;3.<\/p>\n\n\n\n<p>Finally,&nbsp;include the negative sign to get the negative square&nbsp;root.<\/p>\n\n\n\n<p>The&nbsp;negative square root of&nbsp;9&nbsp;is&nbsp;\u20133.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/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\/95327\/844\/666\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1.png\" alt=\"\" class=\"wp-image-7076\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-1-150x150.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\/75571\/565\/687\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1.png\" alt=\"\" class=\"wp-image-7077\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Square roots key notes : Introduction to Square Roots: Perfect Squares: \u221a0 0 \u221a1 1 \u221a4 2 \u221a9 3 \u221a16 4 \u221a25 5 \u221a36 6 \u221a49 7 \u221a64 8 \u221a81 9 \u221a100 10 \u221a121 11 \u221a144 12 \u221a169 13 \u221a196 14 \u221a225 15 \u221a256 16 \u221a289 17 \u221a324 18 \u221a361 19 \u221a400 20 Estimating Square<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/a-5-square-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.5 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-20","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":32,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions"}],"predecessor-version":[{"id":18246,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/20\/revisions\/18246"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}