Решебник по алгебре 8 класс Мерзляк ФГОС Задание 897

 

\[\boxed{\mathbf{897\ (897).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{18 + 8\sqrt{2}} =\]

\[= \sqrt{2 + 16 + 8\sqrt{2}} =\]

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

\[2)\ \sqrt{38 - 12\sqrt{2}} =\]

\[= \sqrt{2 + 36 - 12\sqrt{2}} =\]

\[= \sqrt{\left( \sqrt{2} - 6 \right)^{2}} = \left| \sqrt{2} - 6 \right| =\]

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

\[3)\sqrt{16 + 6\sqrt{7}} + \sqrt{23 - 8\sqrt{7}} =\]

\[= \sqrt{\left( \sqrt{7} + 3 \right)^{2}} + \sqrt{\left( \sqrt{7} - 4 \right)^{2}} =\]

\[= \sqrt{7} + 3 + 4 - \sqrt{7} = 7\]

\[= \sqrt{\left( \sqrt{17} - 3 \right)^{2}} - \sqrt{\left( \sqrt{17} - 7 \right)^{2}} =\]

\[= \sqrt{17} - 3 - 7 + \sqrt{17} =\]

\[= 2\sqrt{17} - 10\]

\[= \sqrt{\left( \sqrt{21} + 5 \right)^{2}} + \sqrt{\left( \sqrt{21} - 5 \right)^{2}} =\]

\[= \sqrt{21} + 5 + 5 - \sqrt{21} = 10\]

\[\boxed{\mathbf{8}\mathbf{97}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{\sqrt{512}}{8} = \sqrt{\frac{512}{8}} = \sqrt{64} = 8\]

\[2)\ \frac{\left( 3\sqrt{7} \right)^{2}}{21} = \frac{9 \cdot 7}{21} = 3\]

\[3)\ \sqrt{45} + \sqrt{20} = 3\sqrt{5} + 2\sqrt{5} = 5\sqrt{5}\]

\[4)\ \left( \sqrt{19} - 3 \right)\left( \sqrt{19} + 3 \right) =\]

\[= 19 - 9 = 10\]

\[5)\ \sqrt{5} \cdot \sqrt{72} \cdot \sqrt{30} =\]

\[= \sqrt{5 \cdot 36 \cdot 2 \cdot 2 \cdot 15} =\]

\[= 6 \cdot 2\sqrt{5 \cdot 5 \cdot 3} =\]

\[= 12 \cdot 5\sqrt{3} = 60\sqrt{3}\]

\[6)\ \left( \sqrt{26} + 1 \right)^{2} = 26 + 2\sqrt{26} + 1 =\]

\[= 27 + 2\sqrt{26}.\]