Решебник по алгебре 8 класс Мерзляк ФГОС Задание 552

 

\[\boxed{\mathbf{552\ (552).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\sqrt{11 + 4\sqrt{7}} = \sqrt{7} + 2\]

\[\left( \sqrt{11 + 4\sqrt{7}} \right)^{2} = \left( \sqrt{7} + 2 \right)^{2}\]

\[11 + 4\sqrt{7} = 7 + 4\sqrt{7} + 4\]

\[11 + 4\sqrt{7} = 11 + 4\sqrt{7}\]

\[2)\ \sqrt{14 + 8\sqrt{3}} = \sqrt{8} + \sqrt{6}\]

\[\left( \sqrt{14 + 8\sqrt{3}} \right)^{2} = \left( \sqrt{8} + \sqrt{6} \right)^{2}\]

\[14 + 8\sqrt{3} = 8 + 2\sqrt{48} + 6\]

\[14 + 8\sqrt{3} = 14 + 8\sqrt{3}\]

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

\[1)\ \sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3};\]

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

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

\[4)\ \sqrt{125} = 5\sqrt{5};\]

\[5)\frac{1}{8}\sqrt{96} = \frac{1}{8} \cdot 4\sqrt{6} = \frac{\sqrt{6}}{2};\]

\[6)\ 0,4\sqrt{250} = 0,4 \cdot 5\sqrt{10} =\]

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

\[7) - 2\sqrt{0,18} = - 2 \cdot 3\sqrt{0,02} =\]

\[= - 6\sqrt{0,02} = - 0,6\sqrt{2};\]

\[8)\frac{4}{9}\sqrt{63} = \frac{4}{9} \cdot 3\sqrt{7} = \frac{4\sqrt{7}}{3};\]

\[9)\ 0,8\sqrt{1250} = 0,8 \cdot 25\sqrt{2} =\]

\[= 20\sqrt{2};\]

\[10)\frac{3}{7}\sqrt{98} = \frac{3}{7} \cdot 7\sqrt{2} = 3\sqrt{2};\]

\[11)\ 10\sqrt{0,03} = \sqrt{3};\]

\[12)\ 0,7\sqrt{1000} = 7\sqrt{10}\text{.\ }\]