Algebra Examples

$\sqrt{8} + \sqrt{20} - \sqrt{12}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2)} + \sqrt{20} - \sqrt{12}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2} + \sqrt{20} - \sqrt{12}$

$\sqrt{2^{2} \cdot 2} + \sqrt{20} - \sqrt{12}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{2} + \sqrt{20} - \sqrt{12}$

Step 3

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 3.1

Factor $4$ out of $20$ .

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

Step 3.2

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Factor $4$ out of $12$ .

$2 \sqrt{2} + 2 \sqrt{5} - \sqrt{4 (3)}$

Step 5.2

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

$2 \sqrt{2} + 2 \sqrt{5} - \sqrt{2^{2} \cdot 3}$

$2 \sqrt{2} + 2 \sqrt{5} - \sqrt{2^{2} \cdot 3}$

Step 6

Pull terms out from under the radical.

$2 \sqrt{2} + 2 \sqrt{5} - (2 \sqrt{3})$

Step 7

Multiply $2$ by $- 1$ .

$2 \sqrt{2} + 2 \sqrt{5} - 2 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2} + 2 \sqrt{5} - 2 \sqrt{3}$

Decimal Form:

$3.83646146 \dots$

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