Simplify square root of 12x^8

$\sqrt{12 x^{8}}$

Step 1

Rewrite $12 x^{8}$ as ${(2 x^{4})}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3) x^{8}}$

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

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

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{2^{2} \cdot 3 {(x^{4})}^{2}}$

Move $3$ .

$\sqrt{2^{2} {(x^{4})}^{2} \cdot 3}$

Rewrite $2^{2} {(x^{4})}^{2}$ as ${(2 x^{4})}^{2}$ .

$\sqrt{{(2 x^{4})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$2 x^{4} \sqrt{3}$