Simplify the surd square root 12 x square root 8<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To simplify ( \\sqrt{12} \\times \\sqrt{8} ), we can use the property that (\\sqrt{a} \\times \\sqrt{b} = \\sqrt{a \\times b}). So,<\/p>\n\n\n\n [ [ In this simplification process, we used two main properties of square roots: the multiplication property (\\sqrt{a} \\times \\sqrt{b} = \\sqrt{a \\times b}) and the ability to break down a square root into simpler components if we have a perfect square as a factor.<\/p>\n\n\n\n By rewriting ( \\sqrt{12} \\times \\sqrt{8} ) as (\\sqrt{96}) and then factoring 96 into (16 \\times 6), we could take the square root of 16 directly (since (\\sqrt{16} = 4)) and leave (\\sqrt{6}) as it is because 6 isn\u2019t a perfect square. This approach allows us to express the product in its simplest surd form: (4\\sqrt{6}).<\/p>\n","protected":false},"excerpt":{"rendered":" Simplify the surd square root 12 x square root 8 The Correct Answer and Explanation is : To simplify ( \\sqrt{12} \\times \\sqrt{8} ), we can use the property that (\\sqrt{a} \\times \\sqrt{b} = \\sqrt{a \\times b}). So, [\\sqrt{12} \\times \\sqrt{8} = \\sqrt{12 \\times 8}] Step-by-Step Solution Final Answer [\\sqrt{12} \\times \\sqrt{8} = 4\\sqrt{6}] Explanation […]<\/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-161426","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161426","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=161426"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161426\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\sqrt{12} \\times \\sqrt{8} = \\sqrt{12 \\times 8}
]<\/p>\n\n\n\nStep-by-Step Solution<\/h3>\n\n\n\n
\n
[
12 \\times 8 = 96
]
So, (\\sqrt{12} \\times \\sqrt{8} = \\sqrt{96}).<\/li>\n\n\n\n
To simplify (\\sqrt{96}), we need to break it down into a product of factors, ideally one of which is a perfect square. Let’s factorize 96:
[
96 = 16 \\times 6
]
Since 16 is a perfect square, we can rewrite (\\sqrt{96}) as:
[
\\sqrt{96} = \\sqrt{16 \\times 6} = \\sqrt{16} \\times \\sqrt{6} = 4\\sqrt{6}
]<\/li>\n<\/ol>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
\\sqrt{12} \\times \\sqrt{8} = 4\\sqrt{6}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n