Question

Rationalise the denominator of the following:

$\left(vi\right)\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}$

Answer 1

Given: $\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}$
Multiplying both numerator and denominator by $\sqrt{3}$ to rationalise the denominator.
$=\frac{(\sqrt{2}+\sqrt{5})\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$
$=\frac{\sqrt{2}\times \sqrt{3}+\sqrt{5}\times \sqrt{3}}{3}$
$=\frac{\sqrt{6}+\sqrt{15}}{3}$