Simplify square root of 50a^15

$\sqrt{50 a^{15}}$

Step 1

Rewrite $50 a^{15}$ as ${(5 a^{7})}^{2} \cdot (2 a)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) a^{15}}$

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

$\sqrt{5^{2} \cdot 2 a^{15}}$

Factor out $a^{14}$ .

$\sqrt{5^{2} \cdot 2 (a^{14} a)}$

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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