Simplify square root of 48x^8

$\sqrt{48 x^{8}}$

Step 1

Rewrite $48 x^{8}$ as ${(4 x^{4})}^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) x^{8}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 x^{8}}$

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

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

Move $3$ .

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

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

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

Step 2

Pull terms out from under the radical.

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