538° Вправа 538Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 158

538. Винесіть множник з-під знака кореня:

1) ${\displaystyle \sqrt{8}=}$${\displaystyle \sqrt{4\cdot 2}=}$${\displaystyle \sqrt{4}\cdot \sqrt{2}=}$${\displaystyle 2\sqrt{2}}$;

2) ${\displaystyle \sqrt{32}=}$${\displaystyle \sqrt{16\cdot 2}=}$${\displaystyle \sqrt{16}\cdot \sqrt{2}=}$${\displaystyle 4\sqrt{2}}$;

3) ${\displaystyle \sqrt{72}=}$${\displaystyle \sqrt{36\cdot 2}=}$${\displaystyle \sqrt{36}\cdot \sqrt{2}=}$${\displaystyle 6\sqrt{2}}$;

4) ${\displaystyle \sqrt{162}=}$${\displaystyle \sqrt{81\cdot 2}=}$${\displaystyle \sqrt{81}\cdot \sqrt{2}=}$${\displaystyle 9\sqrt{2}}$;

5) ${\displaystyle \sqrt{12}=}$${\displaystyle \sqrt{4\cdot 3}=}$${\displaystyle \sqrt{4}\cdot \sqrt{3}=}$${\displaystyle 2\sqrt{3}}$;

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

7) ${\displaystyle \sqrt{75}=}$${\displaystyle \sqrt{25\cdot 3}=}$${\displaystyle \sqrt{25}\cdot \sqrt{3}=}$${\displaystyle 5\sqrt{3}}$;

8) ${\displaystyle \sqrt{128}=}$${\displaystyle \sqrt{64\cdot 2}=}$${\displaystyle \sqrt{64}\cdot \sqrt{2}=}$${\displaystyle 8\sqrt{2}}$;

9) ${\displaystyle \sqrt{20}=}$${\displaystyle \sqrt{4\cdot 5}=}$${\displaystyle \sqrt{4}\cdot \sqrt{5}=}$${\displaystyle 2\sqrt{5}}$;

10) ${\displaystyle \sqrt{125}=}$${\displaystyle \sqrt{25\cdot 5}=}$${\displaystyle \sqrt{25}\cdot \sqrt{5}=}$${\displaystyle 5\sqrt{5}}$;

11) ${\displaystyle \sqrt{250}=}$${\displaystyle \sqrt{25\cdot 10}=}$${\displaystyle \sqrt{25}\cdot \sqrt{10}=}$${\displaystyle 5\sqrt{10}}$;

12) ${\displaystyle \sqrt{500}=}$${\displaystyle \sqrt{100\cdot 5}=}$${\displaystyle \sqrt{100}\cdot \sqrt{5}=}$${\displaystyle 10\sqrt{5}}$;

13) ${\displaystyle \sqrt{300}=}$${\displaystyle \sqrt{100\cdot 3}=}$${\displaystyle \sqrt{100}\cdot \sqrt{3}=}$${\displaystyle 10\sqrt{3}}$;

14) ${\displaystyle \sqrt{80}=}$${\displaystyle \sqrt{16\cdot 5}=}$${\displaystyle \sqrt{16}\cdot \sqrt{5}=}$${\displaystyle 4\sqrt{5}}$;

15) ${\displaystyle \sqrt{180}=}$${\displaystyle \sqrt{36\cdot 5}=}$${\displaystyle \sqrt{36}\cdot \sqrt{5}=}$${\displaystyle 6\sqrt{5}}$;

16) ${\displaystyle \sqrt{405}=}$${\displaystyle \sqrt{81\cdot 5}=}$${\displaystyle \sqrt{81}\cdot \sqrt{5}=}$${\displaystyle 9\sqrt{5}}$.