Решебник по алгебре 8 класс Мерзляк ФГОС Задание 582

 

\[\boxed{\mathbf{582\ (582).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[y = \sqrt{x}\]

\[1)\ y = \sqrt{0,16} = 0,4;\ \ \ \ \ \]

\[y = \sqrt{64} = 8;\ \ \ \ \ \]

\[y = \sqrt{1,44} = 1,2\]

\[y = \sqrt{3600} = 60.\]

\[2)\ 0,2 = \sqrt{x};\ \ \ x = 0,04;\ \ \ \ \]

\[5 = \sqrt{x};\ \ \ \ \ x = 25\]

\[120 = \sqrt{x};\ \ \ \ \ x = \sqrt{14400};\ \ \ \ \]

\[- 4 = \sqrt{x} \Longrightarrow нет\ таких\ x\text{.\ }\]

\[\boxed{\mathbf{5}\mathbf{8}\mathbf{2}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{a - b}{\sqrt{11b} - \sqrt{11a}} =\]

\[= \frac{\left( \sqrt{a} - \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right)}{\sqrt{11} \cdot \left( \sqrt{b} - \sqrt{a} \right)} =\]

\[= \frac{- \sqrt{a} - \sqrt{b}}{- \sqrt{11}} = - \frac{\sqrt{a} + \sqrt{b}}{11}\]

\[2)\ \frac{2a + 10\sqrt{2ab} + 25b}{6a - 75b} =\]

\[= \frac{\left( \sqrt{2a} + 5\sqrt{b} \right)^{2}}{3 \cdot (2a - 25b)} =\]

\[= \frac{\sqrt{2a} + 5\sqrt{b}}{3 \cdot (\sqrt{2a} - 5\sqrt{b})}\]

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

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

\[= \frac{1}{\sqrt{a} + 2}\]