Решебник по алгебре 8 класс Мерзляк ФГОС Задание 569

\[\boxed{\mathbf{569\ (569).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

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

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

\[2)\ \sqrt{7 + 4\sqrt{3}} = \sqrt{4 + 4\sqrt{3} + 3} =\]

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

\[3)\ \sqrt{11 + 2\sqrt{30}} =\]

\[= \sqrt{6 + 2\sqrt{30} + 5} =\]

\[= \sqrt{(\sqrt{6} + \sqrt{5})²} = \sqrt{6} + \sqrt{5}\]

\[\boxed{\mathbf{5}\mathbf{6}\mathbf{9}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

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

\[2)\frac{18}{\sqrt{6}} = \frac{18\sqrt{6}}{6} = 3\sqrt{6};\]

\[3)\frac{5}{\sqrt{10}} = \frac{5\sqrt{10}}{10} = \frac{\sqrt{10}}{2};\]

\[4)\frac{13}{\sqrt{26}} = \frac{13\sqrt{26}}{26} = \frac{\sqrt{26}}{2};\]

\[5)\frac{30}{\sqrt{15}} = \frac{30\sqrt{15}}{15} = 2\sqrt{15};\]

\[6)\frac{2}{3\sqrt{x}} = \frac{2\sqrt{x}}{3x}\text{.\ }\]