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

Jul 28, 2015

$\sqrt{24 x} \sqrt{6 x}$

which already implies the positive domain of $x$.

You can combine the square roots to get:

$= \sqrt{24 x \cdot 6 x}$

Multiply stuff in the square root:
$= \sqrt{24 \cdot 6 \cdot {x}^{2}}$

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

$= \sqrt{144} x$

$= \textcolor{b l u e}{12 x}$