Simplify square root of 50y^14

$\sqrt{50 y^{14}}$

Step 1

Rewrite $50 y^{14}$ as ${(5 y^{7})}^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) y^{14}}$

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

$\sqrt{5^{2} \cdot 2 y^{14}}$

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

$\sqrt{5^{2} \cdot 2 {(y^{7})}^{2}}$

Move $2$ .

$\sqrt{5^{2} {(y^{7})}^{2} \cdot 2}$

Rewrite $5^{2} {(y^{7})}^{2}$ as ${(5 y^{7})}^{2}$ .

$\sqrt{{(5 y^{7})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$5 y^{7} \sqrt{2}$