ГДЗ по алгебре 8 класс Макарычев Задание 487

\[\boxed{\text{487\ (487).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \sqrt{a^{4}b^{4}} = \left| a^{2} \right| \cdot \left| b^{2} \right| = a^{2}b^{2}.\]

\[\textbf{б)}\ \sqrt{b^{6}c^{8}} = \left| b^{3} \right|\left| c^{4} \right| = b^{3}c^{4};\ \ \ \]

\[при\ b \geq 0.\]

\[\textbf{в)}\ \sqrt{16x^{4}y^{12}} = 4\left| x^{2} \right|\left| y^{6} \right| =\]

\[= 4x^{2}y^{6}.\]

\[\textbf{г)}\ \sqrt{0,25p^{2}y^{6}} = 0,5|p|\left| y^{3} \right| =\]

\[= - 0,5py^{3};\ \ при\ p \geq 0;\ \ y \leq 0.\]

\[\textbf{д)}\ \sqrt{\frac{p^{4}}{a^{8}}} = \frac{|p^{2}|}{|a^{4}|} = \frac{p^{2}}{a^{4}}.\]

\[\textbf{е)}\ \sqrt{\frac{16a^{12}}{b^{10}}} = \frac{4\left| a^{6} \right|}{\left| b^{5} \right|} = \frac{4a^{6}}{b^{5}};\ \ \]

\[при\ b > 0.\]

\[\textbf{ж)}\ \sqrt{\frac{4x^{2}}{y^{6}}} = \frac{2|x|}{\left| y^{3} \right|} = \frac{( - 2x)}{- y^{3}} = \frac{2x}{y^{3}};\ \ \]

\[при\ x < 0,\ \ \ y < 0.\]

\[\textbf{з)}\ \sqrt{\frac{c^{6}}{9a^{2}}} = \frac{\left| c^{3} \right|}{3|a|} = \frac{- c^{3}}{3a} = - \frac{c^{3}}{3a};\ \ \]

\[при\ с < 0,\ \ \ a > 0.\]