Question

Express $\frac{1}{\sqrt{5}+\sqrt{2}}$ with rational denominator.

Answer 1

Let, $x=\frac{1}{\sqrt{5}+\sqrt{2}}\times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}$ {rationalizing}

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

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

$\therefore x=\frac{\sqrt{5}}{3}-\frac{\sqrt{2}}{3}$