639° Вправа 639Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 191

639. Винесіть множник з-під знака кореня:

1) ${\displaystyle x>0}$: ${\displaystyle \sqrt{2x^2}=}$${\displaystyle \left|x\right|\sqrt{2}=}$${\displaystyle x\sqrt{2}}$;

2) ${\displaystyle a<0}$: ${\displaystyle \sqrt{3a^2}=}$${\displaystyle \left|a\right|\sqrt{3}=}$${\displaystyle -a\sqrt{3}}$;

3) ${\displaystyle m>0}$: ${\displaystyle \sqrt{8m^2}=}$${\displaystyle \sqrt{4\cdot 2m^2}=}$${\displaystyle 2\left|m\right|\sqrt{2}=}$${\displaystyle 2m\sqrt{2}}$;

4) ${\displaystyle a<0}$: ${\displaystyle \sqrt{a^{2}b}=}$${\displaystyle \left|a\right|\sqrt{b}=}$${\displaystyle -a\sqrt{b}}$;

5) ${\displaystyle a>0}$: ${\displaystyle \sqrt{a^{2}b}=}$${\displaystyle \left|a\right|\sqrt{b}=}$${\displaystyle a\sqrt{b}}$;

6) ${\displaystyle x>0}$, ${\displaystyle y<0}$: ${\displaystyle \sqrt{5x^2{y}^2}=}$${\displaystyle \left|x\right|\left|y\right|\sqrt{5}=}$${\displaystyle x(-y)\sqrt{5}=}$${\displaystyle -xy\sqrt{5}}$;

7) ${\displaystyle x<0}$, ${\displaystyle y>0}$: ${\displaystyle \sqrt{5x^2{y}^2}=}$${\displaystyle \left|x\right|\left|y\right|\sqrt{5}=}$${\displaystyle (-x)y\sqrt{5}=}$${\displaystyle -xy\sqrt{5}}$;

8) ${\displaystyle x>0}$, ${\displaystyle y\ge 0}$: ${\displaystyle \sqrt{50x^2{y}^2}=}$${\displaystyle \sqrt{25\cdot 2x^2{y}^2}=}$${\displaystyle 5\left|x\right|\left|y\right|\sqrt{2}=}$${\displaystyle 5xy\sqrt{2}}$;

9) ${\displaystyle x<0}$, ${\displaystyle y<0}$: ${\displaystyle \sqrt{50x^2{y}^2}=}$${\displaystyle 5\left|x\right|\left|y\right|\sqrt{2}=}$${\displaystyle 5(-x)(-y)\sqrt{2}=}$${\displaystyle 5xy\sqrt{2}}$;

10) ${\displaystyle \sqrt{18x^{4}y}=}$${\displaystyle \sqrt{9\cdot 2\cdot {\left(x^2\right)}^2\cdot y}=}$${\displaystyle 3x^2\sqrt{2y}}$;

11) ${\displaystyle \sqrt{x^8{y}^{4}z}=}$${\displaystyle \sqrt{{\left(x^4\right)}^2\cdot {\left(y^2\right)}^2\cdot z}=}$${\displaystyle x^4{y}^2\sqrt{z}}$;

12) ${\displaystyle \sqrt{a^{20}{b}^{16}c}=}$${\displaystyle \sqrt{{\left(a^{10}\right)}^2\cdot {\left(b^8\right)}^2\cdot c}=}$${\displaystyle a^{10}{b}^8\sqrt{c}}$.