Convert 8(2\/3) into radical form. Then, show your steps and simplify. (Your final answer will be an integer.) Select the “Insert” drop-down option in the menu below and use “\u221a Equation” to type your answer when you need to incorporate symbols, equations, or other math expressions.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To convert ( 8\\left(\\frac{2}{3}\\right) ) into radical form and simplify it to an integer, we can follow these steps:<\/p>\n\n\n\n First, express ( 8 ) as a fraction: Next, multiply the fractions: To express ( \\frac{16}{3} ) in radical form, we want to express it as a square root: To simplify ( \\sqrt{48} ):<\/p>\n\n\n\n Now substitute back into the expression: At this point, we can recognize that ( \\frac{4\\sqrt{3}}{3} ) does not yield an integer. However, if the goal is to convert ( 8\\left(\\frac{2}{3}\\right) ) to an integer without radical form, we can simply multiply: For clarity, if we wanted a precise integer outcome from ( 8 \\left( \\frac{2}{3} \\right) ), we see: Thus, ( 8\\left(\\frac{2}{3}\\right) ) does not simplify to an integer in radical form, yielding a decimal approximately equal to ( 5.33 ). If taken as a whole number, it is simply ( 5 ).<\/p>\n\n\n\n Final Answer: Convert 8(2\/3) into radical form. Then, show your steps and simplify. (Your final answer will be an integer.) Select the “Insert” drop-down option in the menu below and use “\u221a Equation” to type your answer when you need to incorporate symbols, equations, or other math expressions. The Correct Answer and Explanation is: To convert ( […]<\/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-159445","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159445","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=159445"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159445\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159445"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159445"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Rewrite the Expression<\/h3>\n\n\n\n
[
8\\left(\\frac{2}{3}\\right) = \\frac{8}{1} \\times \\frac{2}{3}
]<\/p>\n\n\n\nStep 2: Multiply the Fractions<\/h3>\n\n\n\n
[
\\frac{8 \\times 2}{1 \\times 3} = \\frac{16}{3}
]<\/p>\n\n\n\nStep 3: Convert to Radical Form<\/h3>\n\n\n\n
[
\\frac{16}{3} = \\frac{16}{3} \\cdot \\frac{3}{3} = \\frac{48}{9}
]
Now we can take the square root of the numerator and denominator:
[
\\sqrt{\\frac{48}{9}} = \\frac{\\sqrt{48}}{\\sqrt{9}} = \\frac{\\sqrt{48}}{3}
]<\/p>\n\n\n\nStep 4: Simplify the Square Root<\/h3>\n\n\n\n
\n
[
\\sqrt{48} = \\sqrt{16 \\times 3} = \\sqrt{16} \\cdot \\sqrt{3} = 4\\sqrt{3}
]<\/li>\n<\/ol>\n\n\n\nStep 5: Substitute Back<\/h3>\n\n\n\n
[
\\frac{\\sqrt{48}}{3} = \\frac{4\\sqrt{3}}{3}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
[
8 \\cdot \\frac{2}{3} = \\frac{16}{3} \\approx 5.33 \\quad \\text{(non-integer)}
]<\/p>\n\n\n\n
[
\\text{Rounded down: } 5
]<\/p>\n\n\n\n
[
5
]<\/p>\n","protected":false},"excerpt":{"rendered":"