Simplify square root of 75v^14

$\sqrt{75 v^{14}}$

Step 1

Rewrite $75 v^{14}$ as ${(5 v^{7})}^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) v^{14}}$

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

$\sqrt{5^{2} \cdot 3 v^{14}}$

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

$\sqrt{5^{2} \cdot 3 {(v^{7})}^{2}}$

Move $3$ .

$\sqrt{5^{2} {(v^{7})}^{2} \cdot 3}$

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

$\sqrt{{(5 v^{7})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$5 v^{7} \sqrt{3}$