a) \(=x^2y.\dfrac{\sqrt{xy}}{y}=x^2\sqrt{xy}\)
b) \(=\dfrac{x^2}{y}.\dfrac{\sqrt{y}}{x\sqrt{x}}=\dfrac{x^2}{y}.\dfrac{\sqrt{xy}}{x^2}=\dfrac{\sqrt{xy}}{y}\)
c) \(=\sqrt{\dfrac{5x^2+x^2}{5}}=\sqrt{\dfrac{6x^2}{5}}=\dfrac{\sqrt{30}\left|x\right|}{5}\)
d) \(=\sqrt{\dfrac{12}{20}}+\dfrac{\sqrt{60}}{60}-\dfrac{\sqrt{15}}{15}=\dfrac{\sqrt{15}}{5}+\dfrac{\sqrt{15}}{30}\dfrac{6\sqrt{15}+\sqrt{15}-2\sqrt{15}}{30}=\dfrac{5\sqrt{15}}{30}=\dfrac{\sqrt{15}}{6}\)
a: \(x^2y\cdot\sqrt{\dfrac{x}{y}}=\sqrt{x^4y^2\cdot\dfrac{x}{y}}=\sqrt{x^5y}\)
b: \(\dfrac{x^2}{y}\cdot\sqrt{\dfrac{y}{x^3}}=\dfrac{x^2}{y}\cdot\dfrac{\sqrt{y}}{x\sqrt{x}}=\dfrac{\sqrt{x}}{\sqrt{y}}\)
c: \(\sqrt{x^2+\dfrac{x^2}{5}}=\sqrt{\dfrac{6x^2}{5}}=\dfrac{\sqrt{30}}{5}x\)
