Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $12$ by $2$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Multiply $- 5$ by $2$ .

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

Step 1.7

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

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

Step 1.8

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

$24 - 10 + 2 \cdot 2$

Step 1.9

Multiply $2$ by $2$ .

$24 - 10 + 4$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $10$ from $24$ .

$14 + 4$

Step 2.2

Add $14$ and $4$ .

$18$