825 Вправа 825Алгебра 8 клас Бевз 2025 · § 16 · стор. 155

825. Внеси множник під знак кореня, якщо m < 0.

а) ${\displaystyle m\sqrt{m^2}=}$${\displaystyle -\left|m\right|\sqrt{m^2}=}$${\displaystyle -\sqrt{m^2\cdot m^2}=}$${\displaystyle -\sqrt{m^4}}$;

б) ${\displaystyle 2m\sqrt{\frac{1}{m^2}}=}$${\displaystyle -2\left|m\right|\sqrt{\frac{1}{m^2}}=}$${\displaystyle -\sqrt{\frac{4m^2}{m^2}}}$=

=${\displaystyle -\sqrt{4}=}$${\displaystyle -2}$;

в) ${\displaystyle m^2\sqrt{\frac{3}{m^4}}=}$${\displaystyle \sqrt{\frac{3m^4}{m^4}}=}$${\displaystyle \sqrt{3}}$;

г) ${\displaystyle m^3\sqrt{\frac{1}{m^8}}=}$${\displaystyle -\left|m^3\right|\sqrt{\frac{1}{m^8}}=}$${\displaystyle -\sqrt{\frac{m^6}{m^8}}=}$${\displaystyle -\sqrt{\frac{1}{m^2}}}$.