Question

Rationalisation of the denominator of $\frac{1}{\sqrt{5}+\sqrt{2}}$ gives

(a)$\frac{1}{\sqrt{10}}$ (b)$\sqrt{5}+\sqrt{2}$ (c)$\sqrt{5}-\sqrt{2}$ (d)$\frac{\sqrt{5}-\sqrt{2}}{3}$

Answer 1

$\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{1(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}=\frac{(\sqrt{5}-\sqrt{2})}{5-2}=\frac{\sqrt{5}-\sqrt{2}}{3}$

Hence, the correct answer is option (d)