Simplify. Remove all perfect squares from inside the square root. 63<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To simplify the square root of 63 and remove all perfect squares from inside the square root, we start by factorizing 63 into its prime factors.<\/p>\n\n\n\n Step 1: Factorize 63<\/strong><\/p>\n\n\n\n The number 63 can be factored as follows:<\/p>\n\n\n\n [ Here, 9 is a perfect square since (9 = 3^2).<\/p>\n\n\n\n Step 2: Rewrite the Square Root<\/strong><\/p>\n\n\n\n We can now rewrite the square root of 63 using the factors we found:<\/p>\n\n\n\n [ Step 3: Apply the Property of Square Roots<\/strong><\/p>\n\n\n\n Using the property of square roots that states (\\sqrt{a \\times b} = \\sqrt{a} \\times \\sqrt{b}), we can separate the square root:<\/p>\n\n\n\n [ Step 4: Simplify the Square Root<\/strong><\/p>\n\n\n\n Next, we simplify (\\sqrt{9}):<\/p>\n\n\n\n [ Now substituting back, we get:<\/p>\n\n\n\n [ Final Answer<\/strong><\/p>\n\n\n\n Thus, the simplified form of (\\sqrt{63}) is:<\/p>\n\n\n\n [ Conclusion<\/strong><\/p>\n\n\n\n In this simplification process, we removed the perfect square (9) from inside the square root, leaving us with (3\\sqrt{7}). This method of breaking down the number into its prime factors and identifying perfect squares is a common technique in simplifying square roots. By consistently applying these steps, one can simplify other square roots in a similar manner, making it easier to work with radical expressions in mathematics.<\/p>\n","protected":false},"excerpt":{"rendered":" Simplify. Remove all perfect squares from inside the square root. 63 The Correct Answer and Explanation is : To simplify the square root of 63 and remove all perfect squares from inside the square root, we start by factorizing 63 into its prime factors. Step 1: Factorize 63 The number 63 can be factored as […]<\/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-153876","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153876","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=153876"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153876\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
63 = 9 \\times 7
]<\/p>\n\n\n\n
\\sqrt{63} = \\sqrt{9 \\times 7}
]<\/p>\n\n\n\n
\\sqrt{63} = \\sqrt{9} \\times \\sqrt{7}
]<\/p>\n\n\n\n
\\sqrt{9} = 3
]<\/p>\n\n\n\n
\\sqrt{63} = 3 \\times \\sqrt{7}
]<\/p>\n\n\n\n
\\sqrt{63} = 3\\sqrt{7}
]<\/p>\n\n\n\n