# How do you simplify (2x sqrt( 2x))(3 sqrt(5x))?

Apr 30, 2016

If $x \ge 0$ then

$\left(2 x \sqrt{2 x}\right) \left(3 \sqrt{5 x}\right) = 6 \sqrt{10} {x}^{2}$

#### Explanation:

I will assume that we are dealing with $x \ge 0$ and Real square roots.

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

$\left(2 x \sqrt{2 x}\right) \left(3 \sqrt{5 x}\right)$

$= 2 x \cdot 3 \cdot \sqrt{2 x \cdot 5 x}$

$= 6 x \sqrt{10 {x}^{2}}$

$= 6 x \sqrt{10} \sqrt{{x}^{2}}$

$= 6 x \sqrt{10} x$

$= 6 \sqrt{10} {x}^{2}$