Algebra Examples

$- \sqrt{44 m^{2} n} - 5 \sqrt{99 m^{2} n}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $44 m^{2} n$ as ${(2 m)}^{2} \cdot (11 n)$ .

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Step 1.1.1

Factor $4$ out of $44$ .

$- \sqrt{4 (11) m^{2} n} - 5 \sqrt{99 m^{2} n}$

Step 1.1.2

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

$- \sqrt{2^{2} \cdot 11 m^{2} n} - 5 \sqrt{99 m^{2} n}$

Step 1.1.3

Move $11$ .

$- \sqrt{2^{2} m^{2} \cdot 11 n} - 5 \sqrt{99 m^{2} n}$

Step 1.1.4

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

$- \sqrt{{(2 m)}^{2} \cdot 11 n} - 5 \sqrt{99 m^{2} n}$

Step 1.1.5

Add parentheses.

$- \sqrt{{(2 m)}^{2} \cdot (11 n)} - 5 \sqrt{99 m^{2} n}$

Step 1.2

Pull terms out from under the radical.

$- (2 m \sqrt{11 n}) - 5 \sqrt{99 m^{2} n}$

Step 1.3

Multiply $2$ by $- 1$ .

$- 2 (m \sqrt{11 n}) - 5 \sqrt{99 m^{2} n}$

Step 1.4

Rewrite $99 m^{2} n$ as ${(3 m)}^{2} \cdot (11 n)$ .

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Step 1.4.1

Factor $9$ out of $99$ .

$- 2 m \sqrt{11 n} - 5 \sqrt{9 (11) m^{2} n}$

Step 1.4.2

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

$- 2 m \sqrt{11 n} - 5 \sqrt{3^{2} \cdot 11 m^{2} n}$

Step 1.4.3

Move $11$ .

$- 2 m \sqrt{11 n} - 5 \sqrt{3^{2} m^{2} \cdot 11 n}$

Step 1.4.4

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

$- 2 m \sqrt{11 n} - 5 \sqrt{{(3 m)}^{2} \cdot 11 n}$

Step 1.4.5

Add parentheses.

$- 2 m \sqrt{11 n} - 5 \sqrt{{(3 m)}^{2} \cdot (11 n)}$

Step 1.5

Pull terms out from under the radical.

$- 2 m \sqrt{11 n} - 5 (3 m \sqrt{11 n})$

Step 1.6

Multiply $3$ by $- 5$ .

$- 2 m \sqrt{11 n} - 15 m \sqrt{11 n}$

Step 2

Subtract $15 m \sqrt{11 n}$ from $- 2 m \sqrt{11 n}$ .

$- 17 m \sqrt{11 n}$