Simplify 12 square root of 4-5 square root of 4+2 square root of 4

$12 \sqrt{4} - 5 \sqrt{4} + 2 \sqrt{4}$

Step 1

Simplify each term.

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

$12 \sqrt{2^{2}} - 5 \sqrt{4} + 2 \sqrt{4}$

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

$12 \cdot 2 - 5 \sqrt{4} + 2 \sqrt{4}$

Multiply $12$ by $2$ .

$24 - 5 \sqrt{4} + 2 \sqrt{4}$

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

$24 - 5 \sqrt{2^{2}} + 2 \sqrt{4}$

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

$24 - 5 \cdot 2 + 2 \sqrt{4}$

Multiply $- 5$ by $2$ .

$24 - 10 + 2 \sqrt{4}$

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

$24 - 10 + 2 \sqrt{2^{2}}$

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

$24 - 10 + 2 \cdot 2$

Multiply $2$ by $2$ .

$24 - 10 + 4$

Step 2

Simplify by adding and subtracting.

Subtract $10$ from $24$ .

$14 + 4$

Add $14$ and $4$ .

$18$