complex square root 14 over complex square root 77 symbols wont come out but 14 is over 77 fraction<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To compute the given expression:<\/p>\n\n\n\n [ [ The problem involves simplifying a ratio of two square roots. The process follows mathematical conventions to ensure the result is in its simplest and most acceptable form.<\/p>\n\n\n\n First, the property of square roots, (\\frac{\\sqrt{a}}{\\sqrt{b}} = \\sqrt{\\frac{a}{b}}), simplifies the expression into a single square root. This is a standard approach to combine terms under one root, making further simplification easier.<\/p>\n\n\n\n Next, the fraction inside the square root, (\\frac{14}{77}), is reduced by dividing both numerator and denominator by their greatest common divisor, which is 7. Simplifying fractions is an essential step, as it reduces complexity and avoids unnecessarily large numbers.<\/p>\n\n\n\n After simplifying to (\\sqrt{\\frac{2}{11}}), the square root is split again for clarity as (\\frac{\\sqrt{2}}{\\sqrt{11}}). At this point, the denominator contains a square root, which is traditionally rationalized. Rationalization is performed to make the denominator a rational number, ensuring the result adheres to conventional mathematical standards.<\/p>\n\n\n\n Multiplying numerator and denominator by (\\sqrt{11}) achieves this, yielding (\\frac{\\sqrt{22}}{11}). This process does not change the value of the expression but transforms it into a more standard form.<\/p>\n\n\n\n The final result, (\\frac{\\sqrt{22}}{11}), is the simplest representation. Rationalizing denominators is common practice in mathematics to improve clarity and alignment with conventions, especially in higher-level work where clear communication of results is vital.<\/p>\n","protected":false},"excerpt":{"rendered":" complex square root 14 over complex square root 77 symbols wont come out but 14 is over 77 fraction The Correct Answer and Explanation is : To compute the given expression: [\\frac{\\sqrt{14}}{\\sqrt{77}}] Step-by-step Solution: Final Answer: [\\frac{\\sqrt{14}}{\\sqrt{77}} = \\frac{\\sqrt{22}}{11}] Explanation (300 Words): The problem involves simplifying a ratio of two square roots. The process follows […]<\/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-184770","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184770","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=184770"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184770\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{\\sqrt{14}}{\\sqrt{77}}
]<\/p>\n\n\n\nStep-by-step Solution:<\/h3>\n\n\n\n
\n
By the property of square roots, (\\frac{\\sqrt{a}}{\\sqrt{b}} = \\sqrt{\\frac{a}{b}}):
[
\\frac{\\sqrt{14}}{\\sqrt{77}} = \\sqrt{\\frac{14}{77}}
]<\/li>\n\n\n\n
Divide the numerator and denominator by their greatest common divisor (GCD), which is 7:
[
\\frac{14}{77} = \\frac{2}{11}
] So, the expression becomes:
[
\\sqrt{\\frac{2}{11}}
]<\/li>\n\n\n\n
Split the square root:
[
\\sqrt{\\frac{2}{11}} = \\frac{\\sqrt{2}}{\\sqrt{11}}
]<\/li>\n\n\n\n
To remove the square root from the denominator, multiply numerator and denominator by (\\sqrt{11}):
[
\\frac{\\sqrt{2}}{\\sqrt{11}} \\cdot \\frac{\\sqrt{11}}{\\sqrt{11}} = \\frac{\\sqrt{22}}{11}
]<\/li>\n<\/ol>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\\frac{\\sqrt{14}}{\\sqrt{77}} = \\frac{\\sqrt{22}}{11}
]<\/p>\n\n\n\n
\n\n\n\nExplanation (300 Words):<\/h3>\n\n\n\n