\[\boxed{\text{410\ (410).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Внесем\ число\ под\ знак\ корня.\]
\[\textbf{а)}\ 7\sqrt{10} = \sqrt{7^{2} \cdot 10} =\]
\[= \sqrt{49 \cdot 10} = \sqrt{490}\]
\[\textbf{б)}\ 5\sqrt{3} = \sqrt{5^{2} \cdot 3} = \sqrt{25 \cdot 3} =\]
\[= \sqrt{75}\]
\[\textbf{в)}\ 6\sqrt{x} = \sqrt{6^{2} \cdot x} = \sqrt{36x}\]
\[\textbf{г)}\ 10\sqrt{y} = \sqrt{10^{2} \cdot y} = \sqrt{100y}\]
\[\textbf{д)}\ 3\sqrt{2a} = \sqrt{3^{2} \cdot 2a} = \sqrt{9 \cdot 2a} =\]
\[= \sqrt{18a}\]
\[\textbf{е)}\ 5\sqrt{3b} = \sqrt{5^{2} \cdot 3b} = \sqrt{25 \cdot 3b} =\]
\[= \sqrt{75b}\]