Question

Rationalise the denominator :

$\frac{1}{3+\sqrt{2}}$

Answer 1

Given $\frac{1}{3+\sqrt{2}}$

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

$=\frac{3-\sqrt{2}}{3^2-{\sqrt{2}}^2}$ Using the formula of $(a+b)(a-b)=a^2-b^2$
$=\frac{3-\sqrt{2}}{9-2}$

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