Question

Simplify $\frac{\sqrt{\frac{200}{3}(-20\sqrt{3})}}{\frac{200}{3}}$

Answer 1

We have,

$\frac{\sqrt{\frac{200}{3}(-20\sqrt{3})}}{\frac{200}{3}}$

$=\frac{\sqrt{\frac{200}{3}}\sqrt{(-20\sqrt{3})}}{\sqrt{\frac{200}{3}}\sqrt{\frac{200}{3}}}$

$=\frac{\sqrt{(-20\sqrt{3})}}{\sqrt{\frac{200}{3}}}$

$=\sqrt{\frac{-20\sqrt{3}}{\frac{200}{3}}}$

$=\sqrt{\frac{-3\sqrt{3}}{10}}$

$=\frac{\sqrt{-3\sqrt{3}}}{\sqrt{10}}\times \frac{\sqrt{10}}{\sqrt{10}}$

$=\frac{\sqrt{-30\sqrt{3}}}{10}$

Hence, this is the answer