Basic Math Examples

$\sqrt{8 + 2 \sqrt{12}}$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$\sqrt{8 + 2 \sqrt{4 (3)}}$

Step 1.2

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

$\sqrt{8 + 2 \sqrt{2^{2} \cdot 3}}$

$\sqrt{8 + 2 \sqrt{2^{2} \cdot 3}}$

Step 2

Pull terms out from under the radical.

$\sqrt{8 + 2 (2 \sqrt{3})}$

Step 3

Multiply $2$ by $2$ .

$\sqrt{8 + 4 \sqrt{3}}$

Step 4

Rewrite $8 + 4 \sqrt{3}$ as $2^{2} (2 + \sqrt{3})$ .

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Step 4.1

Factor $4$ out of $8$ .

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

Step 4.2

Factor $4$ out of $4 \sqrt{3}$ .

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

Step 4.3

Factor $4$ out of $4 (2) + 4 (\sqrt{3})$ .

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

Step 4.4

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.86370330 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$