# How do you simplify (sqrt(20x^4)sqrt(5x))/(sqrt(4x^3))?

Apr 9, 2015

$\sqrt{20 {x}^{4}} = \left(2 x\right) \left(x\right) \cdot \sqrt{5}$
$\sqrt{5 x} = \sqrt{5} \cdot \sqrt{x}$
$\sqrt{4 {x}^{3}} = \left(2 x\right) \cdot \sqrt{x}$

So $\frac{\sqrt{20 {x}^{4}} \sqrt{5 x}}{\sqrt{4 {x}^{3}}}$
can be written as
((2x)(x)(sqrt(5))(sqrt(5))(sqrt(x)))/((2x)(sqrt(x))

Simplifying:
((cancel(2x))(x)(sqrt(5))(sqrt(5))(cancel(sqrt(x))))/(cancel((2x))(cancel(sqrt(x)))
and combining the two $\sqrt{5}$ components:

$\frac{\sqrt{20 {x}^{4}} \sqrt{5 x}}{\sqrt{4 {x}^{3}}} = 5 x$