Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor out $m^{2}$ .

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

Step 1.3

Factor out $n^{2}$ .

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

Step 1.4

Move $m$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$8 m n \sqrt{m n}$