{"id":120,"date":"2022-04-12T12:09:51","date_gmt":"2022-04-12T12:09:51","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=120"},"modified":"2025-10-14T10:07:18","modified_gmt":"2025-10-14T10:07:18","slug":"f-16-estimate-positive-and-negative-square-roots","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-16-estimate-positive-and-negative-square-roots\/","title":{"rendered":"F.16 Estimate positive and negative square roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Estimate positive and negative square 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-5305f474ab58a68e3196d48eb437281c\">\ud83c\udf1f<strong> Estimate Positive and Negative 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 Root?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>square root<\/strong> of a number is a value that, when <strong>multiplied by itself<\/strong>, gives the original number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2733\ufe0f <strong>Example<\/strong>: \u221a25 = 5 because 5 \u00d7 5 = 25<\/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>Positive and Negative Square Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Every <strong>positive number<\/strong> has <strong>two square roots<\/strong>:<ul><li>One <strong>positive ( + )<\/strong><\/li><\/ul><\/p>\n\n\n\n<p><ul><li>One <strong>negative ( \u2212 )<\/strong><\/li><\/ul><\/p>\n\n\n\n<p><strong>\u2705 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u221a16 = \u00b14 \u2192 ( +4 and \u22124 ) because<\/li>\n\n\n\n<li>(4 \u00d7 4 = 16) and (\u22124 \u00d7 \u22124 = 16)<\/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>Perfect Squares \ud83d\udfe9<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Numbers like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are <strong>perfect squares<\/strong>.<\/p>\n\n\n\n<p>Their square roots are <strong>whole numbers<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2733\ufe0f <strong>Example<\/strong>: \u221a49 = 7, \u221a81 = 9<\/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>Non-perfect Squares \ud83d\udfe5<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Some numbers (like 2, 3, 5, 6, 7, 8, 10, etc.) are <strong>not perfect squares<\/strong>.<\/p>\n\n\n\n<p>Their square roots are <strong>irrational numbers<\/strong> (non-terminating decimals).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2733\ufe0f <strong>Example<\/strong>: \u221a2 \u2248 1.41, \u221a3 \u2248 1.73<\/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>Estimating Square Roots \ud83d\udd22<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>If a number is <strong>not a perfect square<\/strong>, find <strong>two perfect squares<\/strong> between which the number lies.<\/p>\n\n\n\n<p>\ud83d\udcd8 <strong>Steps:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find two nearest perfect squares.<\/li>\n\n\n\n<li>Find their square roots.<\/li>\n\n\n\n<li>The square root of your number will be <strong>between<\/strong> those two values.<\/li>\n<\/ol>\n\n\n\n<p>\u2705 <strong>Example 1:<\/strong> Estimate \u221a50<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>49 &lt; 50 &lt; 64<\/li>\n\n\n\n<li>\u221a49 = 7 and \u221a64 = 8<br>\ud83d\udc49 So \u221a50 \u2248 7.1<\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>Example 2:<\/strong> Estimate \u221a8<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 &lt; 8 &lt; 9<\/li>\n\n\n\n<li>\u221a4 = 2 and \u221a9 = 3<br>\ud83d\udc49 So \u221a8 \u2248 2.8<\/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>\ud83d\udd39 <strong>Estimating Negative Square Roots \ud83d\udeab<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>negative square root<\/strong> just means <strong>the negative value<\/strong> of the positive root.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2733\ufe0f <strong>Example<\/strong>: \u221a9 = \u00b13 \u2192 Positive root = 3, Negative root = \u22123<\/li>\n\n\n\n<li>\u2733\ufe0f \u221a50 \u2248 \u00b17.1 \u2192 Positive \u2248 +7.1, Negative \u2248 \u22127.1<\/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\udd39 <strong>Square Roots of Negative Numbers \u274c<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>You <strong>cannot find real square roots<\/strong> of negative numbers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2733\ufe0f <strong>Example<\/strong>: \u221a(\u22129) is <strong>not a real number<\/strong>.<\/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\udccf <strong>Helpful Tip:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>You can <strong>use a number line<\/strong> to visualize the position of square roots between two whole numbers!<\/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>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>Number<\/th><th>Perfect Squares Between<\/th><th>Estimated \u221a<\/th><th>Positive &amp; Negative<\/th><\/tr><\/thead><tbody><tr><td>8<\/td><td>4 &amp; 9<\/td><td>\u2248 2.8<\/td><td>\u00b12.8<\/td><\/tr><tr><td>20<\/td><td>16 &amp; 25<\/td><td>\u2248 4.5<\/td><td>\u00b14.5<\/td><\/tr><tr><td>50<\/td><td>49 &amp; 64<\/td><td>\u2248 7.1<\/td><td>\u00b17.1<\/td><\/tr><tr><td>90<\/td><td>81 &amp; 100<\/td><td>\u2248 9.5<\/td><td>\u00b19.5<\/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\udca1 <strong>Remember:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Estimating square roots helps you understand the <strong>approximate value<\/strong> of irrational numbers \u2014 useful in <strong>geometry, algebra, and real-life measurements!<\/strong><\/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-b1d8ff3ee3de14982271544f16743094\" style=\"background-color:#f0a4a4\"><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-62ab3482dd9ada828d60cf7bce6fe1dc\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Complete the following statement. Use the integers that are closest to the number in the middle.<\/strong><\/p>\n\n\n\n<p>( ) &lt;-\u221a15&lt; ( )<\/p>\n<\/div><\/div>\n\n\n\n<p>For now, ignore the negative sign. Find the perfect squares that are just below and just above 15.<\/p>\n\n\n\n<p>The perfect square just below 15 is 9:<\/p>\n\n\n\n<p>\u221a9 = 3<\/p>\n\n\n\n<p>The perfect square just above 15 is 16:<\/p>\n\n\n\n<p>\u221a16 = 4<\/p>\n\n\n\n<p>\u221a15 is between&nbsp;\u221a9 and \u221a16 , so \u221a15 is between 3 and 4 .<\/p>\n\n\n\n<p>Finally, include the negative signs. Remember that with negative numbers, larger numbers like -\u221a16 (if you ignore the minus sign) are&nbsp;<em>less<\/em>&nbsp;than smaller numbers.<\/p>\n\n\n\n<p>-\u221a16&lt; &#8211; \u221a15 &lt;-\u221a9 , so -4&lt;-\u221a15&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-4ab25b75425b623120d224faf5d328b0\" style=\"background-color:#89ccf1\"><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-a0afa2227db722a14b6390a222c2e3c4\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Complete the following statement. Use the integers that are closest to the number in the middle.<\/strong><\/p>\n\n\n\n<p>( ) &lt;-\u221a7&lt; ( )<\/p>\n<\/div><\/div>\n\n\n\n<p>For now, ignore the negative sign. Find the perfect squares that are just below and just above 7.<\/p>\n\n\n\n<p>The perfect square just below 7 is 4:<\/p>\n\n\n\n<p>\u221a4 = 2<\/p>\n\n\n\n<p>The perfect square just above 7 is 9:<\/p>\n\n\n\n<p>\u221a9 = 3<\/p>\n\n\n\n<p>\u221a7 is between \u221a4 and \u221a9 , so&nbsp;\u221a7 is between 2 and 3.<\/p>\n\n\n\n<p>Finally, include the negative signs. Remember that with negative numbers, larger numbers like&nbsp;-\u221a9 (if you ignore the minus sign) are&nbsp;<em>less<\/em>&nbsp;than smaller numbers.<\/p>\n\n\n\n<p>-\u221a9&lt;-\u221a7&lt;-\u221a4 , so -3&lt;-\u221a7&lt;-2 .<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-left has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s try some examples! \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\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78204\/239\/506\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-310.png\" alt=\"\" class=\"wp-image-9632\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-310.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-310-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-310-150x150.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\/36175\/754\/446\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-317.png\" alt=\"\" class=\"wp-image-9633\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-317.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-317-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-317-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Estimate positive and negative square roots Key Notes : \ud83c\udf1f Estimate Positive and Negative Square Roots \ud83d\udd39 What is a Square Root? The square root of a number is a value that, when multiplied by itself, gives the original number. \ud83d\udd39 Positive and Negative Square Roots Every positive number has two square roots: One positive<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-16-estimate-positive-and-negative-square-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.16 Estimate positive and negative 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-120","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\/120","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=120"}],"version-history":[{"count":28,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/120\/revisions"}],"predecessor-version":[{"id":21886,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/120\/revisions\/21886"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}