822 Вправа 822Алгебра 8 клас Бевз 2025 · § 16 · стор. 155

822. Винеси множник з-під знака кореня, якщо a < 0, c < 0.

Пам’ятаємо: ${\displaystyle \sqrt{x^2}=}$${\displaystyle \left|x\right|}$; при ${\displaystyle a<0}$: ${\displaystyle \left|a\right|=}$${\displaystyle -a}$;

${\displaystyle \left|a^3\right|=}$${\displaystyle -a^3}$ (непарні степені від’ємні).

а) ${\displaystyle \sqrt{12a^4}=}$${\displaystyle \sqrt{4a^4\cdot 3}=}$${\displaystyle 2a^2\sqrt{3}}$;

б) ${\displaystyle \sqrt{3c^{10}}=}$${\displaystyle \sqrt{c^{10}\cdot 3}=}$${\displaystyle \left|c^5\right|\sqrt{3}=}$${\displaystyle -c^5\sqrt{3}}$;

в) ${\displaystyle -\sqrt{-18a^7}=}$${\displaystyle -\sqrt{9a^6\cdot (-2a)}}$=

=${\displaystyle -3\left|a^3\right|\sqrt{-2a}}$=

=${\displaystyle -3\cdot (-a^3)\sqrt{-2a}=}$${\displaystyle 3a^3\sqrt{-2a}}$;

г) ${\displaystyle -\sqrt{32a^2{c}^8}=}$${\displaystyle -\sqrt{16a^2{c}^8\cdot 2}=}$${\displaystyle -4\left|a\right|c^4\sqrt{2}}$=

=${\displaystyle -4\cdot (-a)c^4\sqrt{2}=}$${\displaystyle 4a{c}^4\sqrt{2}}$;

ґ) ${\displaystyle \sqrt{-48a^{11}{c}^2}=}$${\displaystyle \sqrt{16a^{10}{c}^2\cdot (-3a)}}$=

=${\displaystyle 4\left|a^5\right|\left|c\right|\sqrt{-3a}}$=

=${\displaystyle 4\cdot (-a^5)(-c)\sqrt{-3a}=}$${\displaystyle 4a^{5}c\sqrt{-3a}}$;

д) ${\displaystyle \sqrt{60a^7{c}^9}=}$${\displaystyle \sqrt{4a^6{c}^8\cdot 15ac}}$=

=${\displaystyle 2\left|a^3\right|c^4\sqrt{15ac}=}$${\displaystyle -2a^3{c}^4\sqrt{15ac}}$;

е) ${\displaystyle \sqrt{\frac{20a^4}{-9c}}=}$${\displaystyle \sqrt{\frac{4a^4}{9}\cdot \frac{5}{-c}}=}$${\displaystyle \frac{2a^2}{3}\sqrt{-\frac{5}{c}}}$;

є) ${\displaystyle \sqrt{\frac{27a^{16}}{16c^6}}=}$${\displaystyle \sqrt{\frac{9a^{16}}{16c^6}\cdot 3}=}$${\displaystyle \frac{3a^8}{4\left|c^3\right|}\sqrt{3}=}$${\displaystyle -\frac{3a^8\sqrt{3}}{4c^3}}$.