Question

Which expression is equivalent to sqrt of 25x^9y^3/64x^6y^11? assume x>0 and y>0

Answer 1

$\sqrt{ \dfrac{25x^9y^3}{64x^6y^{11}} } = \\ \\ = \sqrt{ \dfrac{25x^3}{64y^{8}} } \\ \\ = \sqrt{ \dfrac{5\times 5x^2x}{8\times 8y^{4}y^4} } \\ \\ = \dfrac{5x}{8y^4}\sqrt{ x } \\ \\ = \dfrac{5x\sqrt{x}}{8y^4}$