Simplify - square root of 44m^2n-5 square root of 99m^2n

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

Step 1

Simplify each term.

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

Factor $4$ out of $44$ .

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

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

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

Move $11$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Factor $9$ out of $99$ .

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

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

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

Move $11$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 5$ .

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

Step 2

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

$- 17 m \sqrt{11 n}$