Simplify square root of 28w^8

$\sqrt{28 w^{8}}$

Step 1

Rewrite $28 w^{8}$ as ${(2 w^{4})}^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$\sqrt{4 (7) w^{8}}$

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

$\sqrt{2^{2} \cdot 7 w^{8}}$

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

$\sqrt{2^{2} \cdot 7 {(w^{4})}^{2}}$

Move $7$ .

$\sqrt{2^{2} {(w^{4})}^{2} \cdot 7}$

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

$\sqrt{{(2 w^{4})}^{2} \cdot 7}$

Step 2

Pull terms out from under the radical.

$2 w^{4} \sqrt{7}$