7. Освободитесь от иррациональности в знаменателе: a) \frac{5}{3√10}; 6) \frac{8}{√6+√2}

a) $$\frac{5}{3\sqrt{10}} = \frac{5\sqrt{10}}{3\sqrt{10}\sqrt{10}} = \frac{5\sqrt{10}}{3\cdot 10} = \frac{\sqrt{10}}{6}$$

Ответ: $$\frac{\sqrt{10}}{6}$$

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

Ответ: $$2(\sqrt{6}-\sqrt{2})$$