Question

The number obtained by rationalising the denominator of $\frac{1}{\sqrt{7}+2}$ is .

Answer 1

Given: $\frac{1}{\sqrt{7}+2}$

Rationalising the denominator,

$=\frac{(\sqrt{7}-2)}{(\sqrt{7}+2)(\sqrt{7}-2)}$

$=\frac{\sqrt{7}-2}{(\sqrt{7}{)}^2-(2{)}^2}$

$=\frac{\sqrt{7}-2}{7-4}$

$=\frac{\sqrt{7}-2}{3}$