Question

Помогите сократить дробь 5-√5/√10-√50

Answer 1

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