Simplify square root of 48n^9

$\sqrt{48 n^{9}}$

Step 1

Rewrite $48 n^{9}$ as ${(4 n^{4})}^{2} \cdot (3 n)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) n^{9}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 n^{9}}$

Factor out $n^{8}$ .

$\sqrt{4^{2} \cdot 3 (n^{8} n)}$

Rewrite $n^{8}$ as ${(n^{4})}^{2}$ .

$\sqrt{4^{2} \cdot 3 ({(n^{4})}^{2} n)}$

Move $3$ .

$\sqrt{4^{2} {(n^{4})}^{2} \cdot 3 n}$

Rewrite $4^{2} {(n^{4})}^{2}$ as ${(4 n^{4})}^{2}$ .

$\sqrt{{(4 n^{4})}^{2} \cdot 3 n}$

Add parentheses.

$\sqrt{{(4 n^{4})}^{2} \cdot (3 n)}$

Step 2

Pull terms out from under the radical.

$4 n^{4} \sqrt{3 n}$