Question

Освободитесь от иррациональности в знаменателе: $\frac{8}{\sqrt{6}+\sqrt{2}}$

Answer 1

$\frac{8}{\sqrt{6}+\sqrt{2}}=\frac{8(\sqrt{6}-\sqrt{2})  }{(\sqrt{6}+\sqrt{2})(\sqrt{6} -\sqrt{2}) } = \frac{8(\sqrt{6}-\sqrt{2}) }{6-2} =2(\sqrt{6}-\sqrt{2})$

Answer 2

$\frac{8}{ \sqrt{6} + \sqrt{2} } = \frac{8 \times ( \sqrt{6} - \sqrt{2} )}{( \sqrt{6} + \sqrt{2} )( \sqrt{6} - \sqrt{2} )} = \\ \frac{8( \sqrt{6} - \sqrt{2} )}{ 6 - 2} = \frac{8( \sqrt{6} - \sqrt{2} )}{4} = \\ 2( \sqrt{6} - \sqrt{2} ) = 2 \sqrt{6} - 2 \sqrt{2}$