Question

Rationalize the denomination:
$\frac{1}{\sqrt{6}+\sqrt{5}+\sqrt{11}}$

Answer 1

$\frac{1}{\sqrt{6}+\sqrt{5}+\sqrt{11}}=\frac{\sqrt{6}+\sqrt{5}-\sqrt{11}}{(\sqrt{6}+\sqrt{5}{)}^2-11}=\frac{\sqrt{6}+\sqrt{5}-\sqrt{11}}{(6+5+2\sqrt{30})-11}=\frac{\sqrt{6}+\sqrt{5}-\sqrt{11}}{2\sqrt{30}}=\frac{\sqrt{180}+\sqrt{150}-\sqrt{330}}{60}$