Question

$\frac{6 + \sqrt{6} }{ \sqrt{30} + \sqrt{5} }$
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Answer 1

$\frac{6+\sqrt{6}}{\sqrt{30}+\sqrt{5}}=\frac{(\sqrt{6})^2+\sqrt{6}}{\sqrt{6}\sqrt{5}+\sqrt{5}}=\frac{\sqrt{6}(\sqrt{6}+1)}{\sqrt{5}(\sqrt{6}+1)}=\frac{\sqrt{6}}{\sqrt{5}}=\frac{\sqrt{6}\sqrt{5}}{5}=\frac{\sqrt{30}}{5}$