Question

Rationalise the denominators of the following:
$\frac{1}{\sqrt{7}-\sqrt{6}}$

Answer 1

$\frac{1}{\sqrt{7}-\sqrt{6}}$

Multiply numerator and denominator by $\sqrt{7}+\sqrt{6}$

$=\frac{1(\sqrt{7}+\sqrt{6})}{(\sqrt{7}-\sqrt{6})(\sqrt{7}+\sqrt{6})}$

$=\frac{\sqrt{7}+\sqrt{6}}{7-6}$

$=\sqrt{7}+\sqrt{6}$