Simplify square root of 8x^6

$\sqrt{8 x^{6}}$

Step 1

Rewrite $8 x^{6}$ as ${(2 x^{3})}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{6}}$

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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