Simplify square root of 98a^17

$\sqrt{98 a^{17}}$

Step 1

Rewrite $98 a^{17}$ as ${(7 a^{8})}^{2} \cdot (2 a)$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2) a^{17}}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2 a^{17}}$

Factor out $a^{16}$ .

$\sqrt{7^{2} \cdot 2 (a^{16} a)}$

Rewrite $a^{16}$ as ${(a^{8})}^{2}$ .

$\sqrt{7^{2} \cdot 2 ({(a^{8})}^{2} a)}$

Move $2$ .

$\sqrt{7^{2} {(a^{8})}^{2} \cdot 2 a}$

Rewrite $7^{2} {(a^{8})}^{2}$ as ${(7 a^{8})}^{2}$ .

$\sqrt{{(7 a^{8})}^{2} \cdot 2 a}$

Add parentheses.

$\sqrt{{(7 a^{8})}^{2} \cdot (2 a)}$

Step 2

Pull terms out from under the radical.

$7 a^{8} \sqrt{2 a}$