{"id":190,"date":"2022-04-13T10:17:05","date_gmt":"2022-04-13T10:17:05","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=190"},"modified":"2024-08-25T08:08:48","modified_gmt":"2024-08-25T08:08:48","slug":"j-3-solve-a-quadratic-equation-using-square-roots","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-3-solve-a-quadratic-equation-using-square-roots\/","title":{"rendered":"J.3 Solve a quadratic equation using square roots"},"content":{"rendered":"\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Solve a quadratic equation using square roots<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1edc0434a3900ece8f3d094b3efe6d3a\" style=\"color:#e42121\"><strong>Understanding the Square Root Method<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The square root method is a technique for solving quadratic equations that are in the form:\n<ul class=\"wp-block-list\">\n<li><strong>ax\u00b2 = k<\/strong><\/li>\n\n\n\n<li><strong>(x-h)\u00b2 = k<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>This method is especially useful when the quadratic equation doesn&#8217;t have a linear term (bx).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-dbf17a2e0b8fa8a91f3b5759a2897eb3\" style=\"color:#3c7ebf\"><strong>Steps to Solve Using Square Roots<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Isolate the x\u00b2 Term:<\/strong> Ensure the quadratic equation is in the form where the x\u00b2 term is alone on one side.<\/li>\n\n\n\n<li><strong>Apply the Square Root:<\/strong> Take the square root of both sides of the equation. Remember to consider both the positive and negative square roots.<\/li>\n\n\n\n<li><strong>Solve for x:<\/strong> Simplify the square root (if possible) and solve for x.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-85009256b6513f9e6f5ff8ff9b7c5467\" style=\"color:#8dd72b\"><strong>Special Cases<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>No Real Solutions:<\/strong> If k is negative, there are no real solutions.<\/li>\n\n\n\n<li><strong>Zero Solution:<\/strong> If k is zero, the only solution is x = 0.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-75abb8baf7b56fcf4326a153be3b9590\" style=\"color:#af1fe4\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Solve: x\u00b2 = 25<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: x\u00b2 = 25 (already isolated)<\/li>\n\n\n\n<li>Step 2: x = \u00b1\u221a25<\/li>\n\n\n\n<li>Step 3: x = \u00b15<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-344ee98253dc86a7db567c1f6b9d68f8\" style=\"color:#69fb38\"><strong>Key Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The square root method is a direct and efficient way to solve certain quadratic equations.<\/li>\n\n\n\n<li>It&#8217;s applicable when the equation can be expressed in the form of a perfect square.<\/li>\n\n\n\n<li>Always consider both the positive and negative square roots.<\/li>\n\n\n\n<li>Be aware of special cases where there might be no real solutions or a single solution.<\/li>\n<\/ul>\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-large-font-size\" style=\"background-color:#b5eeb5\"><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><strong>Solve for&nbsp;<em>w<\/em>.<\/strong><\/p>\n\n\n\n<p><em>w<\/em><sup>2<\/sup>&nbsp;= 25<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>w<\/em>&nbsp;=&nbsp;________&nbsp;or&nbsp;<em>w<\/em>&nbsp;=________<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em>w<\/em>.<\/p>\n\n\n\n<p><em>w<\/em><sup>2<\/sup> =25<\/p>\n\n\n\n<p>w=\u00b125    <em>Take the square root<\/em><\/p>\n\n\n\n<p>w=\u00b15        <em>Simplify<\/em><\/p>\n\n\n\n<p>w= 5or<em>w<\/em>=-5        <em>Split \u00b1 into + or &#8211;<\/em>      <\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e2f2a4\"><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><strong>Solve for&nbsp;<em>y<\/em>.<\/strong><\/p>\n\n\n\n<p><em>y<\/em><sup>2<\/sup>&nbsp;= 100<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=________or&nbsp;<em>y<\/em>&nbsp;=________<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;y.<\/p>\n\n\n\n<p><sup>y2<\/sup> =100<\/p>\n\n\n\n<p>y=\u00b110   <em>Take the square root<\/em><\/p>\n\n\n\n<p>y=\u00b110        <em>Simplify<\/em><\/p>\n\n\n\n<p>y= 10ory=-10        <em>Split \u00b1 into + or &#8211;<\/em>      <\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1b7f2\"><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><strong>Solve for&nbsp;<em>u<\/em>.<\/strong><\/p>\n\n\n\n<p><em>u<\/em><sup>2<\/sup>&nbsp;= 9<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-fffc98a02690661d477040a522ecb6b1\" style=\"color:#b00012\"><br><strong>Write your answers as integers or as proper or improper fractions in simplest form.<\/strong><\/p>\n\n\n\n<p><em>u<\/em>&nbsp;=________&nbsp;or&nbsp;<em>u<\/em>&nbsp;=&nbsp;________<\/p>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;y.<\/p>\n\n\n\n<p><sup>u2<\/sup> =9<\/p>\n\n\n\n<p>u=\u00b13     <em>Take the square root<\/em><\/p>\n\n\n\n<p>u=\u00b13        <em>Simplify<\/em><\/p>\n\n\n\n<p>u= 3oru=-3        <em>Split \u00b1 into + or &#8211;<\/em>      <\/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\/76677\/392\/415\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50.png\" alt=\"\" class=\"wp-image-6936\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50-150x150.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\/76714\/889\/505\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-68.png\" alt=\"\" class=\"wp-image-6939\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-68.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-68-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-68-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve a quadratic equation using square roots Key Notes : Understanding the Square Root Method Steps to Solve Using Square Roots Special Cases Example Solve: x\u00b2 = 25 Key Points Learn with an example Solve for&nbsp;w. w2&nbsp;= 25 Write your answers as integers or as proper or improper fractions in simplest form. w&nbsp;=&nbsp;________&nbsp;or&nbsp;w&nbsp;=________ Solve for&nbsp;w.<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-3-solve-a-quadratic-equation-using-square-roots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.3 Solve a quadratic equation using 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-190","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=190"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/190\/revisions"}],"predecessor-version":[{"id":13686,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/190\/revisions\/13686"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}