Simplify square root of 128x^3

$\sqrt{128 x^{3}}$

Step 1

Rewrite $128 x^{3}$ as ${(8 x)}^{2} \cdot (2 x)$ .

Factor $64$ out of $128$ .

$\sqrt{64 (2) x^{3}}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 2 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{8^{2} \cdot 2 (x^{2} x)}$

Move $2$ .

$\sqrt{8^{2} x^{2} \cdot 2 x}$

Rewrite $8^{2} x^{2}$ as ${(8 x)}^{2}$ .

$\sqrt{{(8 x)}^{2} \cdot 2 x}$

Add parentheses.

$\sqrt{{(8 x)}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$8 x \sqrt{2 x}$