Решебник по алгебре 8 класс Мерзляк ФГОС Задание 554

 

\[\boxed{\mathbf{554\ (554).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left( 3\sqrt{2} + 1 \right)\left( \sqrt{8} - 2 \right) =\]

\[= 3\sqrt{16} - 6\sqrt{2} + \sqrt{8} - 2 =\]

\[= 12 - 6\sqrt{2} + 2\sqrt{2} - 2 =\]

\[= 10 - 4\sqrt{2};\]

\[2)\ \left( 3 - 2\sqrt{7} \right)^{2} + \left( 3 + 2\sqrt{7} \right)^{2} =\]

\[= 74;\]

\[3)\ \left( 10 - 4\sqrt{6} \right)\left( 2 + \sqrt{6} \right)^{2} =\]

\[= \left( 10 - 4\sqrt{6} \right)\left( 10 + 4\sqrt{6} \right) =\]

\[= 100 - 96 = 4\]

\[4)\ \left( \sqrt{9 - 4\sqrt{2}} + \sqrt{9 + 4\sqrt{2}} \right)^{2} =\]

\[= 18 + 7 \cdot 2 = 18 + 14 = 32.\]

\[\boxed{\mathbf{5}\mathbf{5}\mathbf{4}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 2\sqrt{6} = \sqrt{4 \cdot 6} = \sqrt{24};\]

\[2)\ 9\sqrt{2} = \sqrt{81 \cdot 2} = \sqrt{162};\]

\[3) - 11\sqrt{3} = - \sqrt{363};\]

\[4)\ 12\sqrt{b} = \sqrt{144b};\]

\[5) - 7\sqrt{3c} = - \sqrt{49 \cdot 3c} =\]

\[= - \sqrt{147c};\]

\[6) - 10\sqrt{0,7m} =\]

\[= - \sqrt{100 \cdot 0,7m} = - \sqrt{70m};\]

\[7)\ 8\ \sqrt{\frac{n}{8}} = \sqrt{64\frac{n}{8}} = \sqrt{8n};\]

\[8) - \frac{1}{3}\sqrt{18p} = - \sqrt{\frac{1}{9} \cdot 18p} =\]

\[= - \sqrt{2p}.\]