Question

Rationalise the denominators of the following:
$\frac{1}{3+\sqrt{2}}$

Answer 1

We need to rationalise $\frac{1}{3+\sqrt{2}}$

On multiplying numerator and denominator by $3-\sqrt{2}$, we get

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

$=\frac{3-\sqrt{3}}{9-2}$

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