Question

Помогите сократить дробь 5-√5/√10-√50

Answer 1

$\tt \dfrac{5-\sqrt{5} }{\sqrt{10}- \sqrt{50}}=\dfrac{5-\sqrt{5} }{\sqrt{10}- 5\sqrt{2}}=\dfrac{(5-\sqrt{5})(\sqrt{10}+5\sqrt{2})}{(\sqrt{10}- 5\sqrt{2})(\sqrt{10}+5\sqrt{2})}=\\\\\\=\dfrac{5\sqrt{10}+25\sqrt{2}-\sqrt{50}-5\sqrt{10}}{10-50}=\dfrac{25\sqrt{2}-5\sqrt{2}}{-40}=-\dfrac{20\sqrt{2}}{40}=-\dfrac{\sqrt{2}}{2}$