Question

Rationalise the denominator and simplify:
$\frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}-\sqrt{3}}$

Answer 1

Solution:

Rationalisation of denominator:

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

$=\frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}-\sqrt{3}}\times \frac{\sqrt{6}+\sqrt{3}}{\sqrt{6}+\sqrt{3}}$

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

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

$=\frac{9+6\sqrt{2}}{3}$

$=3+2\sqrt{2}$