Algebra Examples

$12 \sqrt{m n^{2}} + 5 \sqrt{n^{2}} + 2 \sqrt{m^{3} n^{3}}$

Step 1

Reorder $m$ and $n^{2}$ .

$12 \sqrt{n^{2} m} + 5 \sqrt{n^{2}} + 2 \sqrt{m^{3} n^{3}}$

Step 2

Pull terms out from under the radical.

$12 (n \sqrt{m}) + 5 \sqrt{n^{2}} + 2 \sqrt{m^{3} n^{3}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$12 n \sqrt{m} + 5 n + 2 \sqrt{m^{3} n^{3}}$

Step 4

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

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Step 4.1

Factor out $m^{2}$ .

$12 n \sqrt{m} + 5 n + 2 \sqrt{m^{2} m n^{3}}$

Step 4.2

Factor out $n^{2}$ .

$12 n \sqrt{m} + 5 n + 2 \sqrt{m^{2} m (n^{2} n)}$

Step 4.3

Move $m$ .

$12 n \sqrt{m} + 5 n + 2 \sqrt{m^{2} n^{2} m n}$

Step 4.4

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

$12 n \sqrt{m} + 5 n + 2 \sqrt{{(m n)}^{2} m n}$

Step 4.5

Add parentheses.

$12 n \sqrt{m} + 5 n + 2 \sqrt{{(m n)}^{2} (m n)}$

Step 5

Pull terms out from under the radical.

$12 n \sqrt{m} + 5 n + 2 m n \sqrt{m n}$