# Rationalisation of the denominator of

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

Solution:

$\frac{1}{\sqrt{5}+\sqrt{2}}$

Rationalisation of denominator gives

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

Hence, the correct answer is option (d).