Решебник по алгебре 8 класс Мерзляк ФГОС Задание 585

 

\[\boxed{\mathbf{585\ (585).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{86} > \sqrt{78}\]

\[2)\ \sqrt{1,4} < \sqrt{1,6}\]

\[3)\ 5 < \sqrt{26}\]

\[4)\ \sqrt{\frac{6}{7}} < 1\]

\[5) - 7 < - \sqrt{48}\]

\[6)\ 3\sqrt{2} > \ \ 2\sqrt{3};\ \ \ \ \ \]

\[\sqrt{18} > \sqrt{12}\]

\[7)\ \sqrt{41} > 2\sqrt{10};\ \ \ \ \ \]

\[\sqrt{41} > \sqrt{40}\]

\[8)\ 0,6\sqrt{3\frac{1}{3}} > \text{\ \ }\sqrt{1,1};\ \ \ \ \ \]

\[\sqrt{1,2} > \sqrt{1,1}\]

\[9)\ \sqrt{75} > 4\sqrt{3};\ \ \ \]

\[\sqrt{75} > \sqrt{48}\ \]

\[\boxed{\mathbf{5}\mathbf{8}\mathbf{5}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{1}{5 - 2\sqrt{6}} + \frac{1}{5 + 2\sqrt{6}} = 10\]

\[\frac{5 + 2\sqrt{6} + 5 - 2\sqrt{6}}{\left( 5 - 2\sqrt{6} \right)\left( 5 + 2\sqrt{6} \right)} = 10\]

\[\frac{10}{25 - 24} = 10\]

\[10 = 10.\]

\[2)\ \frac{2}{3\sqrt{2} + 4} - \frac{2}{3\sqrt{2} - 4} = - 8\]

\[\frac{6\sqrt{2} - 8 - 6\sqrt{2} - 8}{\left( 3\sqrt{2} + 4 \right)\left( 3\sqrt{2} - 4 \right)} = - 8\]

\[\frac{- 16}{18 - 16} = - 8\]

\[- \frac{16}{2} = - 8\]

\[- 8 = - 8.\]

\[3)\ \frac{\sqrt{2} + 1}{\sqrt{2} - 1} - \frac{\sqrt{2} - 1}{\sqrt{2} + 1} = 4\sqrt{2}\]

\[\frac{\left( \sqrt{2} + 1 \right)^{2} - \left( \sqrt{2} - 1 \right)^{2}}{\left( \sqrt{2} - 1 \right)\left( \sqrt{2} + 1 \right)} = 4\sqrt{2}\]

\[\frac{2 + \sqrt{2} + 1 - 2 + 2\sqrt{2} - 1}{2 - 1} = 4\sqrt{2}\]

\[\frac{4\sqrt{2}}{1} = 4\sqrt{2}\]

\[4\sqrt{2} = 4\sqrt{2}.\]