662 Вправа 662Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 194

662. Винесіть множник з-під знака кореня:

1) ${\displaystyle \sqrt{54x^2}=}$${\displaystyle \sqrt{9\cdot 6\cdot x^2}=}$${\displaystyle 3\left|x\right|\sqrt{6}}$;

2) ${\displaystyle y\le 0}$: ${\displaystyle \sqrt{-0,4x^2{y}^5}=}$${\displaystyle \sqrt{x^2\cdot y^4\cdot (-0,4y)}=}$${\displaystyle \left|x\right|y^2\sqrt{-0,4y}}$;

3) ${\displaystyle x\ge 0}$: ${\displaystyle \sqrt{\frac{12x^5}{49y^{12}}}=}$${\displaystyle \frac{\sqrt{4x^4\cdot 3x}}{\sqrt{49y^{12}}}=}$${\displaystyle \frac{2x^2\sqrt{3x}}{7y^6}}$;

4) ${\displaystyle \sqrt{\frac{p^{12}}{m{n}^{10}}}=}$${\displaystyle \frac{\sqrt{p^{12}}}{\sqrt{n^{10}}\cdot \sqrt{m}}=}$${\displaystyle \frac{p^6}{\left|n^5\right|\sqrt{m}}}$.