[tex]\it a)\ \sqrt{72a^2} = \sqrt{36\cdot2a^2}=6|a|\sqrt{2},\ \ a\in\mathbb{R}\\ \\ b)\ \sqrt{2a^8}=\sqrt{2(a^4)^2} =a^4\sqrt{2}a\in\mathbb{R}\\ \\ \\ c)\ \sqrt{18a^3b^2} = \sqrt{9\cdot2a^2ab^2}=3a|b|\sqrt{2a},\ \ a\geq0,\ \ b\in\mathbb{R}\\ \\ \\ d)\ \sqrt{\dfrac{25a^3}{27b^5}}= \sqrt{\dfrac{25a^2a}{9\cdot3(b^2)^2b}}=\dfrac{5a\sqrt a}{3b^2\sqrt{3b}},\ \ a\geq0,\ \ b>0[/tex]
