Question

Rationalise the denominator $\frac{\sqrt{3}}{\sqrt{5+\sqrt{2}}}$

Answer 1

We have,

$\frac{\sqrt{3}}{\sqrt{5}+\sqrt{2}}$

$=\frac{\sqrt{3}}{\sqrt{5}+\sqrt{2}}\times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}$

$=\frac{\sqrt{3}(\sqrt{5}-\sqrt{2})}{5-2}$

$=\frac{\sqrt{3}(\sqrt{5}-\sqrt{2})}{3}$

$=\frac{(\sqrt{5}-\sqrt{2})}{\sqrt{3}}$

Hence, the value is $\frac{(\sqrt{5}-\sqrt{2})}{\sqrt{3}}$.