Question

Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4\sqrt{2}}$

Answer 1

Given: $\frac{3+\sqrt{2}}{4\sqrt{2}}$

Dividing numerator and denominator by $\sqrt{2}$

$=\frac{(3+\sqrt{2})\left(\sqrt{2}\right)}{4\sqrt{2}\left(\sqrt{2}\right)}$

$=\frac{3\sqrt{2}+\sqrt{2}\sqrt{2}}{4\times 2}$

$=\frac{3\sqrt{2}+2}{8}$