Решебник по алгебре 8 класс Мерзляк ФГОС Задание 550

 

\[\boxed{\mathbf{550\ (550).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\sqrt{98} - \sqrt{50} + \sqrt{32} =\]

\[= 7\sqrt{2} - 5\sqrt{2} + 4\sqrt{2} = 6\sqrt{2};\]

\[2)\ 3\sqrt{8} + \sqrt{128} - \frac{1}{3}\sqrt{162} =\]

\[= 6\sqrt{2} + 8\sqrt{2} - 3\sqrt{2} = 11\sqrt{2};\]

\[3)\ 0,7\sqrt{300} - 7\sqrt{\frac{3}{49}} + \frac{2}{3}\sqrt{108} =\]

\[= 7\sqrt{3} - \sqrt{3} + 4\sqrt{3} = 10\sqrt{3};\]

\[4)\ \sqrt{5a} - 2\sqrt{20a} + 3\sqrt{80a} =\]

\[= \sqrt{5a} - 4\sqrt{5a} + 12\sqrt{5a} =\]

\[= 9\sqrt{5a};\]

\[5)\ \sqrt{a^{3}b} - \frac{2}{a}\sqrt{a^{5}b} =\]

\[= a\sqrt{\text{ab}} - 2a\sqrt{\text{ab}} = - a\sqrt{\text{ab}};\]

\[6)\ \sqrt{c^{5}} + 4c\sqrt{c^{3}} - 5c^{2}\sqrt{c} =\]

\[= c^{2}\sqrt{c} + 4c^{2}\sqrt{c} - 5c^{2}\sqrt{c} = 0.\]

\[\boxed{\mathbf{5}\mathbf{5}\mathbf{0}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2};\]

\[2)\ \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3};\]

\[3)\ \sqrt{32} = \sqrt{4 \cdot 8} = \sqrt{16 \cdot 2} = 4\sqrt{2};\]

\[4)\ \sqrt{54} = \sqrt{9 \cdot 6} = 3\sqrt{6};\]

\[5)\ \sqrt{490} = \sqrt{49 \cdot 10} = 7\sqrt{10};\]

\[6)\ \sqrt{500} = \sqrt{100 \cdot 5} = 10\sqrt{5};\]

\[7)\ \sqrt{275} = \sqrt{25 \cdot 11} = 5\sqrt{11};\]

\[8)\ \sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3};\]

\[9)\ \sqrt{0,72} = \sqrt{9 \cdot 0,08} =\]

\[= \sqrt{9 \cdot 4 \cdot 0,02} = 6\sqrt{0,02} =\]

\[= 6\sqrt{\frac{2}{100}} = 0,6\sqrt{2};\]

\[10)\ \sqrt{0,48} = \sqrt{16 \cdot 0,03} =\]

\[= 4\sqrt{0,03} = 0,4\sqrt{3};\]

\[11)\ \sqrt{450} = \sqrt{225 \cdot 2} = 15\sqrt{2};\]

\[12)\ \sqrt{36300} = \sqrt{100 \cdot 121 \cdot 3} =\]

\[= 110\sqrt{3}\text{.\ }\]