Question

Rationalise the denominator and simplify:

If $\frac{12\sqrt{2}}{\sqrt{3}+\sqrt{6}}$ is $8\sqrt{3}-m\sqrt{6}$, then $m$ is ?

Answer 1

We rationalize the denominator, $\frac{12\sqrt{2}}{\sqrt{6}+\sqrt{3}}\times \frac{\sqrt{6}-\sqrt{3}}{\sqrt{6}-\sqrt{3}}=\frac{12(\sqrt{12}-\sqrt{6})}{6-3}=4(\sqrt{12}-\sqrt{6})=8\sqrt{3}-4\sqrt{6}$
$\therefore$ value of $m=4$