Question

Rationalise the denominators of the following:
$\frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}$

Answer 1

$\frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}$

Multiply numerator and denumerator by $\sqrt{3}+\sqrt{2}$ we get

$=\frac{\sqrt{6}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}$

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

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