4. Освободите дробь от знака корня в знаменателе: a) \frac{5}{3\sqrt{10}}; б) \frac{8}{\sqrt{6}+\sqrt{2}}.

a) \frac{5}{3\sqrt{10}} = \frac{5\sqrt{10}}{3\sqrt{10}\sqrt{10}} = \frac{5\sqrt{10}}{3 \cdot 10} = \frac{5\sqrt{10}}{30} = \frac{\sqrt{10}}{6}. б) \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} = \frac{8(\sqrt{6}-\sqrt{2})}{4} = 2(\sqrt{6}-\sqrt{2}) = 2\sqrt{6}-2\sqrt{2}. Ответ: a) \frac{\sqrt{10}}{6}; б) 2√6 - 2√2