Simplify square root of 48y^8

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

Step 1

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

Factor $16$ out of $48$ .

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

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

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

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

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

Move $3$ .

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

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

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

Step 2

Pull terms out from under the radical.

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