566 Вправа 566Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 163

566. Винесіть множник з-під знака кореня:

1) ${\displaystyle \sqrt{0,05}=}$${\displaystyle \sqrt{0,01\cdot 5}=}$${\displaystyle \sqrt{0,01}\cdot \sqrt{5}=}$${\displaystyle 0,1\sqrt{5}}$;

2) ${\displaystyle \sqrt{0,121}=}$${\displaystyle \sqrt{121\cdot 0,001}=}$${\displaystyle \sqrt{121}\cdot \sqrt{0,001}=}$${\displaystyle 11\sqrt{0,001}}$;

3) ${\displaystyle \sqrt{28,9}=}$${\displaystyle \sqrt{289\cdot 0,1}=}$${\displaystyle \sqrt{289}\cdot \sqrt{0,1}=}$${\displaystyle 17\sqrt{0,1}}$;

4) ${\displaystyle \sqrt{\frac{3}{20}}=}$${\displaystyle \sqrt{\frac{1}{4}\cdot \frac{3}{5}}=}$${\displaystyle \sqrt{\frac{1}{4}}\cdot \sqrt{\frac{3}{5}}=}$${\displaystyle \frac{1}{2}\sqrt{\frac{3}{5}}}$;

5) ${\displaystyle \sqrt{\frac{7}{36}}=}$${\displaystyle \sqrt{\frac{1}{36}\cdot 7}=}$${\displaystyle \sqrt{\frac{1}{36}}\cdot \sqrt{7}=}$${\displaystyle \frac{1}{6}\sqrt{7}}$;

6) ${\displaystyle \sqrt{3\frac{4}{15}}=}$${\displaystyle \sqrt{\frac{49}{15}}=}$${\displaystyle \sqrt{49\cdot \frac{1}{15}}=}$${\displaystyle \sqrt{49}\cdot \sqrt{\frac{1}{15}}=}$${\displaystyle 7\sqrt{\frac{1}{15}}}$.