Algebra Examples

$\sqrt{2} + \sqrt{12}$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$\sqrt{2} + \sqrt{4 (3)}$

Step 1.2

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

$\sqrt{2} + \sqrt{2^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

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

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\sqrt{2} + 2 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2} + 2 \sqrt{3}$

Decimal Form:

$4.87831517 \dots$