Question

√10 - √2
_______
√5 - 1

Answer 1

Ответ:

$\frac{ \sqrt{10 } - \sqrt{2} }{ \sqrt{5} - 1 } = \frac{( \sqrt{5} + 1) \times ( \sqrt{10} - \sqrt{2}) }{( \sqrt{5} + 1) \times ( \sqrt{5} - 1)} = \frac{ \sqrt{50} + \sqrt{10} - \sqrt{10} - \sqrt{2} }{5 - 1} = \frac{5 \sqrt{2} - \sqrt{2} }{4} = \frac{4 \sqrt{2} }{4} = \sqrt{2}$