Решебник по алгебре 8 класс Мерзляк ФГОС Задание 535

\[\boxed{\mathbf{535\ (535).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 4\sqrt{700} - 27\sqrt{7} =\]

\[= 40\sqrt{7} - 27\sqrt{7} = 13\sqrt{7};\]

\[2)\ \sqrt{75} - 6\sqrt{3} = 5\sqrt{3} - 6\sqrt{3} =\]

\[= - \sqrt{3};\]

\[3)\ 2\sqrt{50} - 8\sqrt{2} = 10\sqrt{2} - 8\sqrt{2} =\]

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

\[4)\ 5\sqrt{12} - 7\sqrt{3} = 10\sqrt{3} - 7\sqrt{3} =\]

\[= 3\sqrt{3};\]

\[5)\ 3\sqrt{72} - 4\sqrt{2} + 2\sqrt{98} =\]

\[= 18\sqrt{2} - 4\sqrt{2} + 14\sqrt{2} = 28\sqrt{2};\]

\[6)\ \frac{1}{3}\sqrt{108} + \sqrt{363} - \frac{2}{9} \cdot \sqrt{243} =\]

\[= 2\sqrt{3} + 11\sqrt{3} - 2\sqrt{3} = 11\sqrt{3}.\]

\[\boxed{\mathbf{5}\mathbf{3}\mathbf{5}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\sqrt{{6,8}^{2} - {3,2}^{2}} =\]

\[= \sqrt{(6,8 - 3,2)(6,8 + 3,2)} =\]

\[= \sqrt{3,6 \cdot 10} = \sqrt{36} = 6\]

\[2)\ \sqrt{{98,5}^{2} - {97,5}^{2}} =\]

\[= \sqrt{(98,5 - 97,5)(98,5 + 97,5)} =\]

\[= \sqrt{1 \cdot 196} = 14\]

\[3)\ \sqrt{\frac{98}{228^{2} - 164^{2}}} =\]

\[= \sqrt{\frac{98}{(228 - 164)(228 + 164)}} =\]

\[= \sqrt{\frac{98}{64 \cdot 392}} =\]

\[= \sqrt{\frac{1}{64 \cdot 4}} = \frac{1}{8 \cdot 2} = \frac{1}{16}\]