{"id":144209,"date":"2024-09-24T12:38:53","date_gmt":"2024-09-24T12:38:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144209"},"modified":"2024-09-24T12:38:56","modified_gmt":"2024-09-24T12:38:56","slug":"find-all-real-square-roots-of-64","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/find-all-real-square-roots-of-64\/","title":{"rendered":"Find all real square roots of 64"},"content":{"rendered":"\n<p>Find all real square roots of 64<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The square roots of a number (x) are the values that, when multiplied by themselves, yield (x). For the number 64, we can find the real square roots by solving the equation:<\/p>\n\n\n\n<p>[<br>x^2 = 64<br>]<\/p>\n\n\n\n<p>To determine the square roots, we can rewrite the equation:<\/p>\n\n\n\n<p>[<br>x = \\sqrt{64}<br>]<\/p>\n\n\n\n<p>Calculating the principal square root of 64, we find:<\/p>\n\n\n\n<p>[<br>\\sqrt{64} = 8<br>]<\/p>\n\n\n\n<p>This means that 8 is one square root of 64. However, it\u2019s important to recognize that every positive number actually has two real square roots: one positive and one negative. Therefore, the other square root is:<\/p>\n\n\n\n<p>[<br>x = -\\sqrt{64} = -8<br>]<\/p>\n\n\n\n<p>In conclusion, the two real square roots of 64 are (8) and (-8).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding Square Roots<\/strong>: The square root function asks for the number that, when multiplied by itself, produces the original number. For example, since (8 \\times 8 = 64), 8 is a square root of 64. Similarly, because (-8 \\times -8 = 64) (the product of two negative numbers is positive), -8 is also a square root.<\/li>\n\n\n\n<li><strong>Mathematical Notation<\/strong>: The square root symbol (\u221a) typically refers to the principal (or non-negative) square root. Hence, (\\sqrt{64} = 8) gives us the positive root. However, the concept of square roots encompasses both the positive and negative roots.<\/li>\n\n\n\n<li><strong>Verification<\/strong>: To confirm the findings, we can check the products:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(8^2 = 64)<\/li>\n\n\n\n<li>((-8)^2 = 64)<br>Both calculations affirm that both 8 and -8 are correct square roots.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Context of Square Roots<\/strong>: Square roots play an essential role in various mathematical applications, including solving quadratic equations, geometry (e.g., calculating areas), and real-world problems involving distances and areas.<\/li>\n<\/ol>\n\n\n\n<p>In summary, the real square roots of 64 are (8) and (-8), and both are essential for understanding the broader implications of square roots in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find all real square roots of 64 The Correct answer and Explanation is: The square roots of a number (x) are the values that, when multiplied by themselves, yield (x). For the number 64, we can find the real square roots by solving the equation: [x^2 = 64] To determine the square roots, we can [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-144209","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144209","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=144209"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144209\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}