Question

Решите пожалуйста примеры с 41 по 44!

Answer 1

$\frac{15}{\sqrt{3}} = \frac{15 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}=\frac{15 \cdot \sqrt{3}}{3}=5\sqrt{3} \\ \\ \frac{3}{\sqrt{18}}=\frac{3 \cdot \sqrt{18}}{\sqrt{18} \cdot \sqrt{18}}=\frac{3 \cdot \sqrt{2 \cdot 9}}{18}=\frac{3\sqrt{2}}{6}=\frac{\sqrt{2}}{2} \\ \\ \frac{1}{2-\sqrt{2}}= \frac{2+ \sqrt{2}}{(2-\sqrt{2}) \cdot (2+\sqrt{2})}=\frac{2+\sqrt{2}}{4 -2}=\frac{2+\sqrt{2}}{2}=1 +\frac{\sqrt{2}}{2}$

$\\ \\ \frac{3}{\sqrt{5} + \sqrt{2}}=\frac{3 \cdot (\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2}) \cdot (\sqrt{5}-\sqrt{2})}=\frac{3 \cdot (\sqrt{5}-\sqrt{2})}{5-2}=\frac{3 \cdot (\sqrt{5}-\sqrt{2})}{3}=\sqrt{5}-\sqrt{2}$