Вынесите множитель из-под знака корня:

1. а) $$\sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3}$$
2. б) $$\sqrt{\frac{3}{16}} = \frac{\sqrt{3}}{\sqrt{16}} = \frac{\sqrt{3}}{4}$$
3. в) $$\sqrt{\frac{40}{81}} = \frac{\sqrt{40}}{\sqrt{81}} = \frac{\sqrt{4 \cdot 10}}{9} = \frac{2\sqrt{10}}{9}$$
4. г) $$\sqrt{\frac{72}{25}} = \frac{\sqrt{72}}{\sqrt{25}} = \frac{\sqrt{36 \cdot 2}}{5} = \frac{6\sqrt{2}}{5}$$
5. д) $$\sqrt{12\frac{1}{2}} = \sqrt{\frac{25}{2}} = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2}$$
6. е) $$\sqrt{1\frac{1}{4}} = \sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{\sqrt{4}} = \frac{\sqrt{5}}{2}$$
7. ж) $$\sqrt{\frac{x^3}{9}} = \frac{\sqrt{x^2 \cdot x}}{\sqrt{9}} = \frac{x\sqrt{x}}{3}$$
8. з) $$\sqrt{\frac{7a}{16b^2}} = \frac{\sqrt{7a}}{\sqrt{16b^2}} = \frac{\sqrt{7a}}{4b}$$
9. и) $$\sqrt{\frac{3m^3n^2}{4a^2b}} = \frac{\sqrt{m^2 \cdot 3m \cdot n^2}}{\sqrt{4a^2b}} = \frac{mn\sqrt{3m}}{2a\sqrt{b}} = \frac{mn\sqrt{3m} \cdot \sqrt{b}}{2a\sqrt{b} \cdot \sqrt{b}} = \frac{mn\sqrt{3mb}}{2ab}$$
10. к) $$\sqrt{\frac{25x^2y^3}{mn^7}} = \frac{\sqrt{25x^2y^2 \cdot y}}{\sqrt{n^6 \cdot mn}} = \frac{5xy\sqrt{y}}{n^3\sqrt{mn}} = \frac{5xy\sqrt{y} \cdot \sqrt{mn}}{n^3\sqrt{mn} \cdot \sqrt{mn}} = \frac{5xy\sqrt{mny}}{mn^4} = \frac{5xy\sqrt{mny}}{mn^4}$$
11. л) $$\sqrt{\frac{0,1x}{10y^2}} = \sqrt{\frac{x}{100y^2}} = \frac{\sqrt{x}}{\sqrt{100y^2}} = \frac{\sqrt{x}}{10y}$$
12. м) $$\sqrt{\frac{5m^3}{0,5n}} = \sqrt{\frac{10m^3}{n}} = \sqrt{\frac{10m^2 \cdot m}{n}} = m\sqrt{\frac{10m}{n}} = m\frac{\sqrt{10m}}{\sqrt{n}} = m\frac{\sqrt{10m} \cdot \sqrt{n}}{\sqrt{n} \cdot \sqrt{n}} = \frac{m\sqrt{10mn}}{n}$$