Решебник по алгебре 8 класс Мерзляк ФГОС Задание 525

 

\[\boxed{\mathbf{525\ (525).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{2}{3}\sqrt{45} = \frac{2}{3} \cdot 3\sqrt{5} = 2\sqrt{5};\]

\[2)\frac{1}{2}\sqrt{128} = \frac{1}{2} \cdot 8\sqrt{2} = 4\sqrt{2};\]

\[3)\frac{1}{10}\sqrt{200} = \frac{1}{10} \cdot 10\sqrt{2} = \sqrt{2};\]

\[4) - 0,05\sqrt{4400} =\]

\[= - 0,05 \cdot 20\sqrt{11} = - \sqrt{11}.\]

\[\boxed{\mathbf{52}\mathbf{5}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \sqrt{36 \cdot 81} = \sqrt{36} \cdot \sqrt{81} =\]

\[= 6 \cdot 9 = 54.\]

\[2)\ \sqrt{900 \cdot 49} = 30 \cdot 7 = 210.\]

\[3)\ \sqrt{16 \cdot 0,25} = 4 \cdot 0,5 = 2.\]

\[4)\ \sqrt{9 \cdot 1,69} = 3 \cdot 1,3 = 3,9.\]

\[5)\ \sqrt{0,36 \cdot 1,21} =\]

\[= 0,6 \cdot 1,1 = 0,66.\]

\[6)\ \sqrt{5^{2} \cdot 3^{6}} = 5 \cdot 3^{3} =\]

\[= 5 \cdot 27 = 135.\]

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

\[= 16 \cdot 3 = 48.\]

\[8)\ \sqrt{2^{6} \cdot 5^{2}} = 2^{3} \cdot 5 =\]

\[= 8 \cdot 5 = 40.\]

\[9)\ \sqrt{2,25 \cdot 0,04 \cdot 1600} =\]

\[= 1,5 \cdot 0,2 \cdot 40 = 12.\]

\[10)\ \sqrt{13\frac{4}{9}} = \sqrt{\frac{121}{9}} =\]

\[= \frac{11}{3} = 3\frac{2}{3}.\]

\[11)\ \sqrt{1\frac{7}{9} \cdot \frac{4}{25}} =\]

\[= \sqrt{\frac{16}{9} \cdot \frac{4}{25}} = \frac{4}{3} \cdot \frac{2}{5} = \frac{8}{15}.\]

\[12)\ \sqrt{\frac{1}{16} \cdot \frac{9}{25}} = \frac{1}{4} \cdot \frac{3}{5} = \frac{3}{20}\text{.\ }\]