Simplify square root of 50a^13

$\sqrt{50 a^{13}}$

Step 1

Rewrite $50 a^{13}$ as ${(5 a^{6})}^{2} \cdot (2 a)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) a^{13}}$

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

$\sqrt{5^{2} \cdot 2 a^{13}}$

Factor out $a^{12}$ .

$\sqrt{5^{2} \cdot 2 (a^{12} a)}$

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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