Решебник по алгебре 8 класс Мерзляк ФГОС Задание 563

 

\[\boxed{\mathbf{563\ (563).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{- m^{9}} = \sqrt{m^{8} \cdot ( - m)} =\]

\[= m^{4}\sqrt{- m}\]

\[2)\ \sqrt{a^{4}b^{13}} = a^{2}b^{6} \cdot \sqrt{b}\]

\[3)\ \sqrt{4x^{6}y} = - 2x^{3} \cdot \sqrt{y};\ \ x < 0\]

\[4)\ \sqrt{m^{7}n^{7}} = m^{3}n^{3}\sqrt{\text{mn}};\ \ m \leq 0,\]

\[n \leq 0\]

\[5)\ \sqrt{45x^{3}y^{14}} = - 3xy^{7}\sqrt{5x};\ \ \]

\[y < 0\]

\[6)\ \sqrt{64a^{2}b^{9}} = 8ab^{4}\sqrt{b};\ \ \]

\[a > 0\]

\[7)\ \sqrt{242m^{11}b^{18}} =\]

\[= - 11m^{5}b^{9}\sqrt{2m};\ \ \]

\[b < 0\]

\[8)\ \sqrt{- m^{2}n^{2}p^{15}} = - mnp^{7}\sqrt{- p};\ \ \]

\[m > 0,\ n < 0\]

\[\boxed{\mathbf{5}\mathbf{6}\mathbf{3}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{7} \cdot \left( \sqrt{7} - \sqrt{28} \right) =\]

\[= \sqrt{49} - \sqrt{196} = 7 - 14 = - 7;\]

\[2)\ \left( \sqrt{18} + \sqrt{72} \right) \cdot \sqrt{2} =\]

\[= \sqrt{36} + \sqrt{144} = 6 + 12 = 18;\]

\[3)\ \left( 4\sqrt{3} - \sqrt{75} + 4 \right) \cdot 3\sqrt{3} =\]

\[= \left( 4\sqrt{3} - 5\sqrt{3} + 4 \right) \cdot 3\sqrt{3} =\]

\[= \left( - \sqrt{3} + 4 \right) \cdot 3\sqrt{3} =\]

\[= - 3\sqrt{9} + 12\sqrt{3} = - 9 + 12\sqrt{3};\]

\[4)\ \left( \sqrt{600} + \sqrt{6} - \sqrt{24} \right) \cdot \sqrt{6} =\]

\[= \left( 10\sqrt{6} + \sqrt{6} - 2\sqrt{6} \right) \cdot \sqrt{6} =\]

\[= 9\sqrt{6} \cdot \sqrt{6} = 54.\]