# How do you simplify sqrt(3x^3) * sqrt(6x^2)?

Sep 3, 2015

$\sqrt{3 {x}^{3}} \cdot \sqrt{6 {x}^{2}} = \sqrt{18 {x}^{5}} = 3 x \sqrt{2 x}$

(assuming $x \ge 0$)

#### Explanation:

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

In our case, if both sqrt's are Real, then:

$\sqrt{3 {x}^{3}} \cdot \sqrt{6 {x}^{2}} = \sqrt{3 {x}^{3} \cdot 6 {x}^{2}} = \sqrt{18 {x}^{5}} = \sqrt{{\left(3 {x}^{2}\right)}^{2} \cdot 2 x}$

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