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

The correct option is D $\frac{(\sqrt{5}-\sqrt{2})}{3}$

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

So correct answer will be option D