Simplify square root of 12x^3

$\sqrt{12 x^{3}}$

Step 1

Rewrite $12 x^{3}$ as ${(2 x)}^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3) x^{3}}$

Rewrite $4$ as $2^{2}$ .

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

Factor out $x^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$2 x \sqrt{3 x}$

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