Question

Question 5 (iii)
Rationalize the denominators of the following:

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

Answer 1

Multiply and divide with $(\sqrt{5}-\sqrt{2}).$
$\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{1(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}=\frac{\sqrt{5}-\sqrt{2}}{(\sqrt{5}{)}^2-(\sqrt{2}{)}^2}=\frac{\sqrt{5}-\sqrt{2}}{5-2}=\frac{\sqrt{5}-\sqrt{2}}{3}$