Simplify: $ \sqrt{432}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3} $

Given:

 \( \sqrt{432}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3} \)

To do:

We have to simplify \( \sqrt{432}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3} \).
Solution:

 $\sqrt{432}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3}=\sqrt{36\times4\times3}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3}$

$=6\times2\sqrt3-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3}$

$=12\sqrt3-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3}$

$=\frac{2\sqrt3\times12\sqrt3-5+2\sqrt3\times4\sqrt3}{2\sqrt3}$

$=\frac{24\times3-5+8\times3}{2\sqrt3}$

$=\frac{72-5+24}{2\sqrt3}$

$=\frac{91}{2\sqrt3}$

$=\frac{91\sqrt3}{2\sqrt3\times\sqrt3}$

$=\frac{91\sqrt3}{6}$
 Therefore,

$\sqrt{432}-\frac{5}{2} \sqrt{\frac{1}{3}}+4 \sqrt{3}=\frac{91\sqrt3}{6}$.

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Updated on: 10-Oct-2022

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