Simplify square root of 32y^12

$\sqrt{32 y^{12}}$

Step 1

Rewrite $32 y^{12}$ as ${(4 y^{6})}^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) y^{12}}$

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

$\sqrt{4^{2} \cdot 2 y^{12}}$

Rewrite $y^{12}$ as ${(y^{6})}^{2}$ .

$\sqrt{4^{2} \cdot 2 {(y^{6})}^{2}}$

Move $2$ .

$\sqrt{4^{2} {(y^{6})}^{2} \cdot 2}$

Rewrite $4^{2} {(y^{6})}^{2}$ as ${(4 y^{6})}^{2}$ .

$\sqrt{{(4 y^{6})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$4 y^{6} \sqrt{2}$