Algebra Examples

$\sqrt{\frac{36}{4} m^{9} n^{3}}$

Step 1

Combine $\frac{36}{4}$ and $m^{9}$ .

$\sqrt{\frac{36 m^{9}}{4} n^{3}}$

Step 2

Combine $\frac{36 m^{9}}{4}$ and $n^{3}$ .

$\sqrt{\frac{36 m^{9} n^{3}}{4}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Reduce the expression $\frac{36 m^{9} n^{3}}{4}$ by cancelling the common factors.

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Step 3.1.1

Factor $4$ out of $36 m^{9} n^{3}$ .

$\sqrt{\frac{4 (9 m^{9} n^{3})}{4}}$

Step 3.1.2

Factor $4$ out of $4$ .

$\sqrt{\frac{4 (9 m^{9} n^{3})}{4 (1)}}$

Step 3.1.3

Cancel the common factor.

$\sqrt{\frac{4 (9 m^{9} n^{3})}{4 \cdot 1}}$

Step 3.1.4

Rewrite the expression.

$\sqrt{\frac{9 m^{9} n^{3}}{1}}$

Step 3.2

Divide $9 m^{9} n^{3}$ by $1$ .

$\sqrt{9 m^{9} n^{3}}$

Step 4

Rewrite $9 m^{9} n^{3}$ as ${(3 m^{4} n)}^{2} (m n)$ .

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} m^{9} n^{3}}$

Step 4.2

Factor out $m^{8}$ .

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

Step 4.3

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

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

Step 4.4

Factor out $n^{2}$ .

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

Step 4.5

Move $m$ .

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

Step 4.6

Rewrite $3^{2} ({(m^{4})}^{2}) n^{2}$ as ${(3 m^{4} n)}^{2}$ .

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

Step 4.7

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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