What is the product of 8, square root of, 8, end square root8 8 \u200b and 5, square root of, 24, end square root5 24 \u200b in simplest radical form<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the product of ( 8\\sqrt{8} ) and ( 5\\sqrt{24} ) in its simplest radical form, we can follow these steps:<\/p>\n\n\n\n The problem asks for the product of two numbers:<\/p>\n\n\n\n [ We can separate this into two parts: the constant multiplications and the radical parts:<\/p>\n\n\n\n [ First, multiply the constants outside the square roots:<\/p>\n\n\n\n [ Now, multiply the square roots. The product of two square roots can be written as a single square root:<\/p>\n\n\n\n [ Simplify the multiplication inside the square root:<\/p>\n\n\n\n [ Thus, we now have:<\/p>\n\n\n\n [ Next, simplify ( \\sqrt{192} ). To do this, we factor ( 192 ) into its prime factors:<\/p>\n\n\n\n [ We know that ( \\sqrt{64} = 8 ), so:<\/p>\n\n\n\n [ Now, we multiply the constants and the simplified square root:<\/p>\n\n\n\n [ Therefore, the product of ( 8\\sqrt{8} ) and ( 5\\sqrt{24} ) in its simplest radical form is:<\/p>\n\n\n\n [ What is the product of 8, square root of, 8, end square root8 8 \u200b and 5, square root of, 24, end square root5 24 \u200b in simplest radical form The Correct Answer and Explanation is: To find the product of ( 8\\sqrt{8} ) and ( 5\\sqrt{24} ) in its simplest radical form, we can […]<\/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-168603","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168603","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=168603"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168603\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Break down the expression<\/h3>\n\n\n\n
8\\sqrt{8} \\times 5\\sqrt{24}
]<\/p>\n\n\n\n
(8 \\times 5) \\times (\\sqrt{8} \\times \\sqrt{24})
]<\/p>\n\n\n\nStep 2: Multiply the constants<\/h3>\n\n\n\n
8 \\times 5 = 40
]<\/p>\n\n\n\nStep 3: Multiply the square roots<\/h3>\n\n\n\n
\\sqrt{8} \\times \\sqrt{24} = \\sqrt{8 \\times 24}
]<\/p>\n\n\n\n
8 \\times 24 = 192
]<\/p>\n\n\n\n
\\sqrt{8} \\times \\sqrt{24} = \\sqrt{192}
]<\/p>\n\n\n\nStep 4: Simplify the square root of 192<\/h3>\n\n\n\n
192 = 64 \\times 3
]<\/p>\n\n\n\n
\\sqrt{192} = \\sqrt{64 \\times 3} = \\sqrt{64} \\times \\sqrt{3} = 8\\sqrt{3}
]<\/p>\n\n\n\nStep 5: Combine the results<\/h3>\n\n\n\n
40 \\times 8\\sqrt{3} = 320\\sqrt{3}
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
\\boxed{320\\sqrt{3}}
]<\/p>\n","protected":false},"excerpt":{"rendered":"