Simplify square root of 150x^3

$\sqrt{150 x^{3}}$

Step 1

Rewrite $150 x^{3}$ as ${(5 x)}^{2} \cdot (6 x)$ .

Factor $25$ out of $150$ .

$\sqrt{25 (6) x^{3}}$

Rewrite $25$ as $5^{2}$ .

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

Factor out $x^{2}$ .

$\sqrt{5^{2} \cdot 6 (x^{2} x)}$

Move $6$ .

$\sqrt{5^{2} x^{2} \cdot 6 x}$

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt{{(5 x)}^{2} \cdot 6 x}$

Add parentheses.

$\sqrt{{(5 x)}^{2} \cdot (6 x)}$

Step 2

Pull terms out from under the radical.

$5 x \sqrt{6 x}$