Question

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

Answer 1

`sqrt(20x^4) = (2x)(x)*sqrt(5)`
`sqrt(5x) = sqrt(5)*sqrt(x)`
`sqrt(4x^3) = (2x)*sqrt(x)`

So `(sqrt(20x^4)sqrt(5x))/sqrt(4x^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:

`(sqrt(20x^4)sqrt(5x))/sqrt(4x^3) = 5x`