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Julli [10]
3 years ago
8

ChallengESee attachment and answer :)​

Mathematics
1 answer:
jeka943 years ago
8 0

<h3><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u></h3>
  • Simplify:

\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}

<h3><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u> </u><u>:</u><u> </u></h3>

\displaystyle{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}

<u>Step-by-step-explanation:</u>

We have given an expression.

We have to simplify the expression.

The given expression is

\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:4\:\sqrt{16\:\times\:3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}

<h3>We know that,</h3>

\displaystyle{\boxed{\pink{\sf\:\sqrt{a\:\times\:b}\:=\:\sqrt{a}\:\times\:\sqrt{b}\:}}\:\cdots\sf\:a\:,\:b\:\geq\:0}

\displaystyle{\implies\sf\:4\:\sqrt{16}\:\times\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:4\:\times\:4\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}

<h3>We know that,</h3>

\displaystyle{\boxed{\blue{\sf\:\sqrt{\dfrac{a}{b}}\:=\:\dfrac{\sqrt{a}}{\sqrt{b}}\:}}\:\cdots\sf\:b\: > \:0}

\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{\sqrt{1}}{\sqrt{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{1}{\sqrt{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:\dfrac{16\:\sqrt{3}\:\times\:2\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:\dfrac{16\:\times\:2\:\sqrt{3}\:\times\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}} \\  \\\displaystyle{\implies\sf\:\dfrac{32\:\times\:3\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}

\displaystyle{\implies\sf\:\dfrac{8\:\times\:4\:\times\:3\:-\:5\:+\:(\:6\:\sqrt{3}\:\times\:2\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:6\:\times\:2\:\times\:\sqrt{3}\:\times\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:12\:\times\:3\:)}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:12\:\times\:3}{2\:\sqrt{3}}} \\  \\  \\ \displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:+\:12\:\times\:3\:-\:5}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{12\:(\:8\:+\:3\:)\:-\:5}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{12\:\times\:11\:-\:5}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{132\:-\:5}{2\:\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}} \\ \\   \\ \displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}\:\times\:\dfrac{\sqrt{3}}{\sqrt{3}}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{2\:\times\:3}} \\  \\  \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{6}} \\  \\  \\ \displaystyle{\therefore\:\underline{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}}

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