# How do you simplify  sqrt ((75xy^7)/(12xy))?

##### 1 Answer
Jul 23, 2016

$\frac{5}{2} {y}^{3}$

#### Explanation:

$\sqrt{\frac{75 x {y}^{7}}{12 x y}}$
=sqrt((cancel(3)*25*cancel(x)*cancel(y)*y^6)/(cancel(3)*4*cancel(x)*cancel(y)) {cancelling out common terms in numerator and denominator, and using law of indices ${x}^{a} \cdot {x}^{b} = {x}^{a + b}$}
$= \sqrt{{\left(5 {y}^{3}\right)}^{2} / {2}^{2}}$
$= {\left(\frac{5}{2} {y}^{3}\right)}^{2 \cdot \frac{1}{2}}${using the fact that square roots are same as power 1/2, cube roots as power 1/3 and nth roots are same as power 1/n}
$= \frac{5}{2} {y}^{3}$