570 Вправа 570Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 164

570. Спростіть вираз:

1) ${\displaystyle \frac{\sqrt{24}-\sqrt{3}}{2\sqrt{2}-1}=}$${\displaystyle \frac{\sqrt{3}(2\sqrt{2}-1)}{2\sqrt{2}-1}=}$${\displaystyle \sqrt{3}}$;

2) ${\displaystyle \frac{\sqrt{8}+\sqrt{6}}{\sqrt{3}+2}=}$${\displaystyle \frac{\sqrt{2}(2+\sqrt{3})}{\sqrt{3}+2}=}$${\displaystyle \sqrt{2}}$;

3) ${\displaystyle \frac{\sqrt{0,81}+\sqrt{27}}{\sqrt{0,27}+3}=}$${\displaystyle \frac{0,9+3\sqrt{3}}{0,3\sqrt{3}+3}=}$${\displaystyle \frac{\sqrt{3}(0,3\sqrt{3}+3)}{0,3\sqrt{3}+3}=}$${\displaystyle \sqrt{3}}$;

4) ${\displaystyle \frac{5}{\sqrt{2}+3\sqrt{3}}+\frac{5}{\sqrt{2}-3\sqrt{3}}=}$${\displaystyle \frac{5(\sqrt{2}-3\sqrt{3})+5(\sqrt{2}+3\sqrt{3})}{2-27}=}$${\displaystyle \frac{10\sqrt{2}}{-25}=}$${\displaystyle -0,4\sqrt{2}}$.