Question

Rationalise the denominator and simplify $\frac{3\sqrt{5}}{\sqrt{6}}$

Answer 1

The given surd is $\frac{3\sqrt{5}}{\sqrt{6}}$

We rationalise the denominator of $\frac{3\sqrt{5}}{\sqrt{6}}$ by multiplying $\sqrt{6}$ in the numerator and denominator as follows:

$\frac{3\sqrt{5}}{\sqrt{6}}\times \frac{\sqrt{6}}{\sqrt{6}}$

$\Rightarrow \frac{3\sqrt{30}}{\sqrt{36}}$

$\Rightarrow \frac{3\sqrt{30}}{6}$

$\Rightarrow \frac{\sqrt{30}}{2}$

Hence, $\frac{3\sqrt{5}}{\sqrt{6}}=\frac{\sqrt{30}}{2}$