Simplify square root of 50u^14

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

Step 1

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

Factor $25$ out of $50$ .

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

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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