Вынеси множитель из-под знака корня для каждого выражения.

Вынесем множитель из-под знака корня: а) $$\sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3}$$ б) $$\sqrt{\frac{3}{16}} = \frac{\sqrt{3}}{\sqrt{16}} = \frac{\sqrt{3}}{4}$$ в) $$\sqrt{\frac{40}{81}} = \frac{\sqrt{40}}{\sqrt{81}} = \frac{\sqrt{4 \cdot 10}}{9} = \frac{2\sqrt{10}}{9}$$ г) $$\sqrt{\frac{72}{25}} = \frac{\sqrt{72}}{\sqrt{25}} = \frac{\sqrt{36 \cdot 2}}{5} = \frac{6\sqrt{2}}{5}$$ д) $$\sqrt{12\frac{1}{2}} = \sqrt{\frac{24+1}{2}} = \sqrt{\frac{25}{2}} = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2}$$ е) $$\sqrt{1\frac{1}{4}} = \sqrt{\frac{4+1}{4}} = \sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{\sqrt{4}} = \frac{\sqrt{5}}{2}$$ ж) $$\sqrt{\frac{x^3}{9}} = \frac{\sqrt{x^3}}{\sqrt{9}} = \frac{\sqrt{x^2 \cdot x}}{3} = \frac{|x|\sqrt{x}}{3}$$ (при $x \ge 0$, это будет $\frac{x\sqrt{x}}{3}$) з) $$\sqrt{\frac{7a}{16b^2}} = \frac{\sqrt{7a}}{\sqrt{16b^2}} = \frac{\sqrt{7a}}{4|b|}$$ (при $b \ne 0$ и $a \ge 0$) и) $$\sqrt{\frac{3m^3n^2}{4a^2b}} = \frac{\sqrt{3m^3n^2}}{\sqrt{4a^2b}} = \frac{\sqrt{m^2n^2 \cdot 3m}}{\sqrt{4a^2b}} = \frac{|mn|\sqrt{3m}}{2|a|\sqrt{b}} = \frac{|mn|\sqrt{3m}\sqrt{b}}{2|a|b} = \frac{|mn|\sqrt{3mb}}{2|a|b}$$ (при $b > 0$, $m \ge 0$, $a \ne 0$) к) $$\sqrt{\frac{25x^2y^3}{mn^7}} = \frac{\sqrt{25x^2y^3}}{\sqrt{mn^7}} = \frac{|5x|\sqrt{y^2y}}{\sqrt{n^6n \cdot m}} = \frac{5|x||y|\sqrt{y}}{|n^3|\sqrt{mn}} = \frac{5|xy|\sqrt{y}\sqrt{mn}}{|n^3|mn} = \frac{5|xy|\sqrt{ymn}}{|n^3|mn}$$ (при $m>0, n>0, y \ge 0$) л) $$\sqrt{\frac{0,1x}{10y^2}} = \sqrt{\frac{1x}{100y^2}} = \frac{\sqrt{x}}{\sqrt{100y^2}} = \frac{\sqrt{x}}{10|y|}$$ (при $x \ge 0$, $y \ne 0$) м) $$\sqrt{\frac{5m^3}{0,5n}} = \sqrt{\frac{10m^3}{n}} = \frac{\sqrt{10m^2m}}{\sqrt{n}} = \frac{|m|\sqrt{10m}}{\sqrt{n}} = \frac{|m|\sqrt{10m}\sqrt{n}}{n} = \frac{|m|\sqrt{10mn}}{n}$$ (при $m \ge 0, n > 0$)