Simplify square root of 48n^3

$\sqrt{48 n^{3}}$

Step 1

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

Factor $16$ out of $48$ .

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

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

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

Factor out $n^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$4 n \sqrt{3 n}$

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