\[\boxed{\text{413\ (413).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ 2\sqrt{2} = \sqrt{2^{2}} \cdot \sqrt{2} = \sqrt{4 \cdot 2} =\]
\[= \sqrt{8}\]
\[\textbf{б)}\ 5\sqrt{y} = \sqrt{5^{2}} \cdot \sqrt{y} = \sqrt{25y}\]
\[\textbf{в)} - 7\sqrt{3} = - \sqrt{7^{2}} \cdot \sqrt{3} =\]
\[= - \sqrt{49 \cdot 3} = - \sqrt{147}\]
\[\textbf{г)} - 6\sqrt{2a} = - \sqrt{6^{2}} \cdot \sqrt{2a} =\]
\[= - \sqrt{36 \cdot 2a} = - \sqrt{72a}\]
\[\textbf{д)}\frac{1}{3}\sqrt{18b} = \sqrt{\left( \frac{1}{3} \right)^{2}} \cdot \sqrt{18b} =\]
\[= \sqrt{\frac{1}{9} \cdot 18b} = \sqrt{2b}\]
\[\textbf{е)} - 0,1\sqrt{200c} =\]
\[= - \sqrt{\left( \frac{1}{10} \right)^{2}} \cdot \sqrt{200c} =\]
\[= - \sqrt{\frac{1}{100} \cdot 200c} = - \sqrt{2c}\ \]