Question

Solve $2\sqrt{54}-6\sqrt{\frac{2}{3}}-\sqrt{96}=?$

Answer 1

$2\sqrt{54}-6\sqrt{\frac{2}{3}}-\sqrt{96}$

This can be written as

$\Rightarrow 2\times 3\sqrt{6}-6\sqrt{\frac{2}{3}}-4\sqrt{6}$

$\Rightarrow 6\sqrt{6}-6\sqrt{\frac{2}{3}}-4\sqrt{6}$

$\Rightarrow 2\sqrt{6}-6\frac{\sqrt{2}}{\sqrt{3}}$

$\Rightarrow 2\sqrt{2}\sqrt{3}-6\frac{\sqrt{2}}{\sqrt{3}}$

$\Rightarrow \frac{2\sqrt{2}\times 3-6\sqrt{2}}{\sqrt{3}}$

$\Rightarrow \frac{6\sqrt{2}-6\sqrt{2}}{\sqrt{3}}=0$