Question

Rationalise the denomination $\frac{1}{7+3\sqrt{2}}$

Answer 1

Given $=\frac{1}{7+3\sqrt{2}}$ $\times \frac{7-3\sqrt{2}}{7-3\sqrt{2}}$
$=\frac{7-3\sqrt{2}}{7^2-(3\sqrt{2}{)}^2}$ Using $(a-b)(a+b)=a^2-b^2$

$=\frac{7-3\sqrt{2}}{49-18}$

$=\frac{7-3\sqrt{2}}{31}$

$=\frac{7}{31}-\frac{3\sqrt{2}}{31}$