Simplify square root of 50v^12

$\sqrt{50 v^{12}}$

Step 1

Rewrite $50 v^{12}$ as ${(5 v^{6})}^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) v^{12}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 v^{12}}$

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

$\sqrt{5^{2} \cdot 2 {(v^{6})}^{2}}$

Move $2$ .

$\sqrt{5^{2} {(v^{6})}^{2} \cdot 2}$

Rewrite $5^{2} {(v^{6})}^{2}$ as ${(5 v^{6})}^{2}$ .

$\sqrt{{(5 v^{6})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$5 v^{6} \sqrt{2}$