Algebra Examples

$\sqrt{12} + \sqrt{48}$

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 $12$ .

$\sqrt{4 (3)} + \sqrt{48}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 3} + \sqrt{48}$

$\sqrt{2^{2} \cdot 3} + \sqrt{48}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{3} + \sqrt{48}$

Step 1.3

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.3.1

Factor $16$ out of $48$ .

$2 \sqrt{3} + \sqrt{16 (3)}$

Step 1.3.2

Rewrite $16$ as $4^{2}$ .

$2 \sqrt{3} + \sqrt{4^{2} \cdot 3}$

$2 \sqrt{3} + \sqrt{4^{2} \cdot 3}$

Step 1.4

Pull terms out from under the radical.

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

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

Step 2

Add $2 \sqrt{3}$ and $4 \sqrt{3}$ .

$6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3}$

Decimal Form:

$10.39230484 \dots$

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