661 Вправа 661Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 194

661. Винесіть множник з-під знака кореня:

1) ${\displaystyle \sqrt{8n^2}=}$${\displaystyle \sqrt{4\cdot 2\cdot n^2}=}$${\displaystyle 2\left|n\right|\sqrt{2}}$;

2) ${\displaystyle z\ge 0}$: ${\displaystyle \sqrt{18x^4{y}^8{z}^7}=}$${\displaystyle \sqrt{9x^4{y}^8{z}^6\cdot 2z}=}$${\displaystyle 3x^2{y}^4{z}^3\sqrt{2z}}$;

3) ${\displaystyle b\ge 0}$: ${\displaystyle \sqrt{0,01a^8{b}^3}=}$${\displaystyle \sqrt{0,01a^8{b}^2\cdot b}=}$${\displaystyle 0,1a^{4}b\sqrt{b}}$;

4) ${\displaystyle x\ge 0}$: ${\displaystyle \sqrt{\frac{8x^3}{125y^{10}}}=}$${\displaystyle \frac{\sqrt{4x^2\cdot 2x}}{\sqrt{25\cdot 5\cdot y^{10}}}=}$${\displaystyle \frac{2x\sqrt{2x}}{5\sqrt{5}\left|y^5\right|}}$;

5) ${\displaystyle n<0}$: ${\displaystyle \sqrt{-\frac{p^4}{m^6{n}^3}}=}$${\displaystyle \sqrt{\frac{p^4}{m^6{n}^2\cdot (-n)}}=}$${\displaystyle \frac{p^2}{-n\left|m^3\right|\sqrt{-n}}}$;

6) ${\displaystyle m>0}$: ${\displaystyle \sqrt{\frac{{(n+3)}^4}{m^5}}=}$${\displaystyle \frac{\sqrt{{\left({(n+3)}^2\right)}^2}}{\sqrt{m^4\cdot m}}=}$${\displaystyle \frac{{\left(n+3\right)}^2}{m^2\sqrt{m}}}$.