Question

Simplification of $\frac{\sqrt{40}}{\sqrt{3}}$ is $\frac{2}{3}\sqrt{m}$, then find the value of $m$

Answer 1

$\frac{\sqrt{40}}{\sqrt{3}}$ $=\frac{\sqrt{40}\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$ $=\frac{\sqrt{120}}{3}$

$=\frac{\sqrt{2\times 2\times 3\times 2\times 5}}{3}$ $=\frac{2\sqrt{30}}{3}$.

Thus, the new value of $m$ is $30$.