Question

Сократите дробь
$\frac{2 \sqrt{5} - 5 \sqrt{2} - \sqrt{10} }{2 - \sqrt{10} - \sqrt{2} }$

Answer 1

$\frac{2\sqrt{5}-5\sqrt{2}-\sqrt{10}}{2-\sqrt{10}-\sqrt{2}}=\frac{\sqrt{4*5}-\sqrt{5*10}-\sqrt{2*5}}{4-\sqrt{10}-\sqrt{2}}=\frac{\sqrt{5}(\sqrt{4}-\sqrt{10}-\sqrt{2})}{4-\sqrt{10}-\sqrt{2}}=\sqrt{5}$