Combine these radicals. -12\u221a12-2\u221a3<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To combine the radicals in the expression (-12\\sqrt{12} – 2\\sqrt{3}), we first need to simplify (-12\\sqrt{12}).<\/p>\n\n\n\n The square root of 12 can be simplified as follows:<\/p>\n\n\n\n [ Now we can substitute this back into the expression:<\/p>\n\n\n\n [ Now we can rewrite the original expression:<\/p>\n\n\n\n [ Since both terms now contain the same radical (\\sqrt{3}), we can combine them:<\/p>\n\n\n\n [ Thus, the simplified expression is:<\/p>\n\n\n\n [ When combining radicals, it\u2019s essential to first simplify any radicals that can be expressed in terms of simpler radicals. The square root of a product, like (\\sqrt{12}), can be broken down using the property that (\\sqrt{a \\cdot b} = \\sqrt{a} \\cdot \\sqrt{b}). In this case, we used this property to simplify (\\sqrt{12}) into (2\\sqrt{3}).<\/p>\n\n\n\n Once we had (-12\\sqrt{12}) simplified to (-24\\sqrt{3}), we were able to see that both terms in the expression shared the radical (\\sqrt{3}). This allowed us to combine them into a single term, which is a crucial technique when working with expressions involving radicals. By following these steps, we ensure the expression is simplified correctly and efficiently.<\/p>\n","protected":false},"excerpt":{"rendered":" Combine these radicals. -12\u221a12-2\u221a3 The Correct Answer and Explanation is : To combine the radicals in the expression (-12\\sqrt{12} – 2\\sqrt{3}), we first need to simplify (-12\\sqrt{12}). Step 1: Simplify (\\sqrt{12}) The square root of 12 can be simplified as follows: [\\sqrt{12} = \\sqrt{4 \\cdot 3} = \\sqrt{4} \\cdot \\sqrt{3} = 2\\sqrt{3}] Step 2: Substitute […]<\/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-153852","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153852","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=153852"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153852\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Simplify (\\sqrt{12})<\/h3>\n\n\n\n
\\sqrt{12} = \\sqrt{4 \\cdot 3} = \\sqrt{4} \\cdot \\sqrt{3} = 2\\sqrt{3}
]<\/p>\n\n\n\nStep 2: Substitute (\\sqrt{12}) in the Expression<\/h3>\n\n\n\n
-12\\sqrt{12} = -12 \\cdot 2\\sqrt{3} = -24\\sqrt{3}
]<\/p>\n\n\n\nStep 3: Rewrite the Expression<\/h3>\n\n\n\n
-12\\sqrt{12} – 2\\sqrt{3} = -24\\sqrt{3} – 2\\sqrt{3}
]<\/p>\n\n\n\nStep 4: Combine Like Terms<\/h3>\n\n\n\n
-24\\sqrt{3} – 2\\sqrt{3} = (-24 – 2)\\sqrt{3} = -26\\sqrt{3}
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
\\boxed{-26\\sqrt{3}}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n