Simplify square root of 12x^6

$\sqrt{12 x^{6}}$

Step 1

Rewrite $12 x^{6}$ as ${(2 x^{3})}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3) x^{6}}$

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

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Move $3$ .

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

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

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

Step 2

Pull terms out from under the radical.

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