Решебник по алгебре 8 класс Мерзляк ФГОС Задание 565

 

\[\boxed{\mathbf{565\ (565).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ a\sqrt{3} = \sqrt{3a^{2}}\]

\[2)\ b\sqrt{- b} = \sqrt{- b^{3}}\]

\[3)\ c\sqrt{c^{5}} = \sqrt{c^{7}}\ \]

\[4)\ m\sqrt{n} = \sqrt{m^{2}n};\ \ m \geq 0\]

\[5)\ xy²\sqrt{\text{xy}} = - \sqrt{x^{3}y^{5}}\]

\[6)\ 2p\sqrt{\frac{p}{2}} = \sqrt{\frac{4p^{3}}{2}} = \sqrt{2p^{3}}\]

\[7)\ 2p\sqrt{- \frac{p}{2}} = - \sqrt{- 2p^{3}}\ \]

\[8)\ ab²\sqrt{\frac{a}{b}} = \sqrt{a^{3}b^{3}},\ \ a \geq 0\]

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

\[1)\ \left( \sqrt{7} + 3 \right)\left( 3\sqrt{7} - 1 \right) =\]

\[= 3 \cdot 7 - \sqrt{7} + 9\sqrt{7} - 3 =\]

\[= 8\sqrt{7} + 18;\]

\[2)\ \left( 4\sqrt{2} - \sqrt{3} \right)\left( 2\sqrt{2} + 5\sqrt{3} \right) =\]

\[= 16 + 20\sqrt{6} - 2\sqrt{6} - 15 =\]

\[= 18\sqrt{6} + 1;\]

\[3)\ \left( \sqrt{p} - q \right)\sqrt{p} + q) = p - q^{2};\]

\[4)\ \left( 6 - \sqrt{13} \right)\left( 6 + \sqrt{13} \right) =\]

\[= 36 - 13 = 23;\]

\[5)\ \left( \sqrt{5} - x \right)\left( \sqrt{5} + x \right) = 5 - x^{2};\]

\[6)\ \left( \sqrt{19} + \sqrt{17} \right)\left( \sqrt{19} - \sqrt{17} \right) =\]

\[= 19 - 17 = 2;\]

\[7)\ \left( \sqrt{6} + \sqrt{2} \right)^{2} = 6 + 2\sqrt{12} + 2 =\]

\[= 4\sqrt{3} + 8;\]

\[8)\ \left( 3 - 2\sqrt{15} \right)² =\]

\[= 9 - 12\sqrt{15} + 60 =\]

\[= 69 - 12\sqrt{15}.\]