{"id":124,"date":"2022-04-12T12:10:24","date_gmt":"2022-04-12T12:10:24","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=124"},"modified":"2025-10-14T10:27:11","modified_gmt":"2025-10-14T10:27:11","slug":"f-18-solve-equations-involving-squares-and-square-roots","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-18-solve-equations-involving-squares-and-square-roots\/","title":{"rendered":"F.18 Solve equations involving squares and square roots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve equations involving squares and 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-c37e64153d5e83fa1212f8d1dad665af\">\ud83c\udf1f<strong> Solve Equations Involving 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 result of multiplying the number by itself.<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>Example<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4<sup>2<\/sup>=4\u00d74=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>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<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> Solving Equations Involving Squares<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>\u2734\ufe0f Example 1:<\/strong><\/h3>\n\n\n\n<p>Solve x<sup>2<\/sup>=49<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Take the square root of both sides <\/p>\n\n\n\n<p class=\"has-text-align-center\">x=\u00b1\u221a49\u200b<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Simplify <\/p>\n\n\n\n<p class=\"has-text-align-center\">x=\u00b17<\/p>\n\n\n\n<p>\u2705 <strong>Final Answer:<\/strong> x=7 or x=\u22127<\/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\udde9 <strong>Solving Equations Involving Square Roots<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>\u2734\ufe0f Example 2:<\/strong><\/h3>\n\n\n\n<p>Solve \u221ax=8<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Square both sides to remove the square root<\/p>\n\n\n\n<p class=\"has-text-align-center\"> (\u221ax)<sup>2<\/sup>=8<sup>2<\/sup><\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Simplify <\/p>\n\n\n\n<p class=\"has-text-align-center\">x=64<\/p>\n\n\n\n<p>\u2705 <strong>Final Answer:<\/strong> x=64<\/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\udde0 <strong>Remember These Important Rules<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2705 When squaring both sides, <strong>check for extraneous solutions<\/strong> (false answers).<\/p>\n\n\n\n<p>\u2705 A <strong>square equation<\/strong> can have <strong>two solutions<\/strong> \u2014 one positive and one negative.<\/p>\n\n\n\n<p>\u2705 A <strong>square root equation<\/strong> has <strong>only non-negative roots<\/strong> (since square root of a number is defined as the principal or positive root).<\/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\udca1 <strong>Common Forms and How to Solve<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Equation Type<\/strong><\/th><th><strong>Example<\/strong><\/th><th><strong>Solution Method<\/strong><\/th><\/tr><\/thead><tbody><tr><td>x<sup>2<\/sup>=a<\/td><td>x<sup>2<\/sup>=36<\/td><td>x=\u00b1\u221a36=\u00b16<\/td><\/tr><tr><td>\u221ax=a<\/td><td>\u221ax=9<\/td><td>x=a<sup>2<\/sup>=81<\/td><\/tr><tr><td>(x\u2212k)<sup>2<\/sup>=a<\/td><td>(x\u22123)<sup>2<\/sup>=16<\/td><td>x\u22123=\u00b14 \u21d2 x=7&nbsp;or&nbsp;\u22121<\/td><\/tr><tr><td>\u221ax+k=a<\/td><td>\u221ax+2=5<\/td><td>x+2=25 \u21d2 x=23<\/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>\u26a0\ufe0f <strong>Check Your Answer<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Always substitute your solution back into the <strong>original equation<\/strong> to verify it satisfies the equation.<\/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>Key Takeaways<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83c\udf08 Squaring removes square roots.<\/p>\n\n\n\n<p>\ud83c\udf08 Taking square roots removes squares.<\/p>\n\n\n\n<p>\ud83c\udf08 Every square equation may have <strong>two solutions<\/strong>.<\/p>\n\n\n\n<p>\ud83c\udf08 Always <strong>check for valid answers<\/strong> after squaring.<\/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-background has-normal-font-size\" style=\"background-color:#013f3f\"><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-bacba98affcddeec19e5717d7984d247\" style=\"color:#b00012\">Solve for&nbsp;<em>k<\/em>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5c712e70ad21e707f963d18d8929853e\" style=\"color:#b00012\"><strong>12 =&nbsp;\u221a<em>k<\/em><\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-8bff440d65399c8fd18c6f6a60b4544b\" style=\"color:#b00012\">k =?<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-8360ee0ec631d73aee1912e055043995\"><br>Solve for&nbsp;<em>k<\/em>.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-a1f3e874d66b4dce4bbed0396e1bce81\">\u221a<em>k<\/em>&nbsp;=&nbsp;12<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-f3778a05d09f9be6c8febdb4f642a815\">(\u221ak)<sup>2 <\/sup><sub>&nbsp;= 12<\/sub><sup>2<\/sup>   &#8212;-&gt; <em>Square both sides<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-00d258a10585143760db6752caa9751a\"><em>k<\/em>&nbsp;=&nbsp;144<em><\/em><br>The solution is 144.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#505304\"><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-69754c58e4a5ebf4680c07a7de6de294\" style=\"color:#b00012\">Solve for&nbsp;<em>z<\/em>.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-909522476b245f6ef6faa1338c1fbfe0\" style=\"color:#b00012\"><strong><em>z<\/em><sup>2<\/sup>&nbsp;= 64<br><\/strong><em>z<\/em>&nbsp;=&nbsp;&nbsp;___ or&nbsp;___<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-05324ff02ae07437adcf39ac782e8ea0\">Solve for&nbsp;<em>z<\/em>.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-799a98e45dc3869802423b8d671cdcef\"><em>z<\/em><sup>2<\/sup>&nbsp;=&nbsp;64<br><em>z<\/em>&nbsp;=&nbsp;\u00b1\u221a64   &#8212;&#8211;&gt; <em>Take the square root of both sides<\/em><br><em>z<\/em>&nbsp;=&nbsp;\u00b18<br>The solutions are 8 and&nbsp;-8.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#4a0202\"><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-b4b867714ee663eb1ea3281d3f477f18\" style=\"color:#b00012\">Solve for&nbsp;j.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-8923ec07933498d6343a73cd2a7bc024\" style=\"color:#b00012\"><strong>\u221aj = 6<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-3efc8a87e11e691430140b24ff7f01d9\" style=\"color:#b00012\">j =<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-a43a0d82673f39c2f42a9976d426dcb9\">Solve for&nbsp;j.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c7d7a21ea1e856b042f2a30e1cca9363\">\u221aj = 6<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-b198d799669a62fc3400afa6389368ae\">( \u221aj)<sup>2<\/sup> = 6<sup>2<\/sup>                   <em>Square both sides<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-bb05f371d4ddd0d72c2fd6a1567a1ab5\">j = 36<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-fdb901bae60251d5787a8e2e26227e57\">The solution is 36 .<\/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\/78207\/559\/250\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-308.png\" alt=\"\" class=\"wp-image-9625\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-308.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-308-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-308-150x150.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\/059\/470\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-315.png\" alt=\"\" class=\"wp-image-9626\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-315.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-315-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-315-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve equations involving squares and square roots Key Notes : \ud83c\udf1f Solve Equations Involving Squares and Square Roots \ud83d\udd39 What is a Square ? The square of a number is the result of multiplying the number by itself. \ud83d\udc49 Example: \ud83d\udd39 What is a Square Root ? The square root of a number is the<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-18-solve-equations-involving-squares-and-square-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.18 Solve equations involving 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-124","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\/124","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=124"}],"version-history":[{"count":28,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/124\/revisions"}],"predecessor-version":[{"id":21893,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/124\/revisions\/21893"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}