565 Вправа 565Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 163

565. Винесіть множник з-під знака кореня:

1) ${\displaystyle \sqrt{0,03}=}$${\displaystyle \sqrt{0,01\cdot 3}=}$${\displaystyle \sqrt{0,01}\cdot \sqrt{3}=}$${\displaystyle 0,1\sqrt{3}}$;

2) ${\displaystyle \sqrt{0,08}=}$${\displaystyle \sqrt{0,04\cdot 2}=}$${\displaystyle \sqrt{0,04}\cdot \sqrt{2}=}$${\displaystyle 0,2\sqrt{2}}$;

3) ${\displaystyle \sqrt{0,169}=}$${\displaystyle \sqrt{0,0169\cdot 10}=}$${\displaystyle \sqrt{0,0169}\cdot \sqrt{10}=}$${\displaystyle 0,13\sqrt{10}}$;

4) ${\displaystyle \sqrt{22,5}=}$${\displaystyle \sqrt{\frac{225}{10}}=}$${\displaystyle \frac{\sqrt{225}}{\sqrt{10}}=}$${\displaystyle \frac{15}{\sqrt{10}}=}$${\displaystyle \frac{15\sqrt{10}}{10}=}$${\displaystyle 1,5\sqrt{10}}$;

5) ${\displaystyle \sqrt{\frac{8}{15}}=}$${\displaystyle \frac{\sqrt{8}}{\sqrt{15}}=}$${\displaystyle \frac{\sqrt{4\cdot 2}}{\sqrt{15}}=}$${\displaystyle \frac{2\sqrt{2}}{\sqrt{15}}=}$${\displaystyle \frac{2\sqrt{2}\cdot \sqrt{15}}{15}=}$${\displaystyle \frac{2\sqrt{30}}{15}}$;

6) ${\displaystyle \sqrt{\frac{45}{49}}=}$${\displaystyle \frac{\sqrt{45}}{\sqrt{49}}=}$${\displaystyle \frac{\sqrt{9\cdot 5}}{7}=}$${\displaystyle \frac{3\sqrt{5}}{7}}$;

7) ${\displaystyle \sqrt{2\frac{2}{7}}=}$${\displaystyle \sqrt{\frac{16}{7}}=}$${\displaystyle \frac{\sqrt{16}}{\sqrt{7}}=}$${\displaystyle \frac{4}{\sqrt{7}}=}$${\displaystyle \frac{4\sqrt{7}}{7}}$;

8) ${\displaystyle \sqrt{1\frac{11}{13}}=}$${\displaystyle \sqrt{\frac{24}{13}}=}$${\displaystyle \frac{\sqrt{4\cdot 6}}{\sqrt{13}}=}$${\displaystyle \frac{2\sqrt{6}}{\sqrt{13}}=}$${\displaystyle \frac{2\sqrt{6}\cdot \sqrt{13}}{13}=}$${\displaystyle \frac{2\sqrt{78}}{13}}$.