Question

How do you simplify: the square root of 24x times the square root of 6x?

Answer 1

Your problem stated:

`sqrt(24x)sqrt(6x)`

which already implies the positive domain of `x`.

You can combine the square roots to get:

`= sqrt(24x*6x)`

Multiply stuff in the square root:
`= sqrt(24*6*x^2)`

Pull `x^2` out by reversing the first step, basically, and evaluating the result:
`= sqrt(24*6)x`
(this is OK without absolute values because the original problem had only positive `sqrtx`.)

`=sqrt(144)x`

`= color(blue)(12x)`