Simplify square root of 64m^3n^3

$\sqrt{64 m^{3} n^{3}}$

Step 1

Rewrite $64 m^{3} n^{3}$ as ${(8 m n)}^{2} (m n)$ .

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} m^{3} n^{3}}$

Factor out $m^{2}$ .

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

Factor out $n^{2}$ .

$\sqrt{8^{2} (m^{2} m) (n^{2} n)}$

Move $m$ .

$\sqrt{8^{2} m^{2} n^{2} m n}$

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

$\sqrt{{(8 m n)}^{2} m n}$

Add parentheses.

$\sqrt{{(8 m n)}^{2} (m n)}$

Step 2

Pull terms out from under the radical.

$8 m n \sqrt{m n}$