Pre-Algebra Examples

$| 3 - \sqrt{12} |$

Step 1

Simplify each term.

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Step 1.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$| 3 - \sqrt{4 (3)} |$

Step 1.1.2

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

$| 3 - \sqrt{2^{2} \cdot 3} |$

Step 1.2

Pull terms out from under the radical.

$| 3 - (2 \sqrt{3}) |$

Step 1.3

Multiply $2$ by $- 1$ .

$| 3 - 2 \sqrt{3} |$

Step 2

$3 - 2 \sqrt{3}$ is approximately $- 0.46410161$ which is negative so negate $3 - 2 \sqrt{3}$ and remove the absolute value

$- (3 - 2 \sqrt{3})$

Step 3

Apply the distributive property.

$- 1 \cdot 3 - (- 2 \sqrt{3})$

Step 4

Multiply $- 1$ by $3$ .

$- 3 - (- 2 \sqrt{3})$

Step 5

Multiply $- 2$ by $- 1$ .

$- 3 + 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 3 + 2 \sqrt{3}$

Decimal Form:

$0.46410161 \dots$