Algebra Examples

$2 (\sqrt{48} + \sqrt{27})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $48$ .

$2 (\sqrt{16 (3)} + \sqrt{27})$

Step 1.1.2

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

$2 (\sqrt{4^{2} \cdot 3} + \sqrt{27})$

$2 (\sqrt{4^{2} \cdot 3} + \sqrt{27})$

Step 1.2

Pull terms out from under the radical.

$2 (4 \sqrt{3} + \sqrt{27})$

Step 1.3

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.3.1

Factor $9$ out of $27$ .

$2 (4 \sqrt{3} + \sqrt{9 (3)})$

Step 1.3.2

Rewrite $9$ as $3^{2}$ .

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

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

Step 1.4

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

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Step 2.1

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

$2 (7 \sqrt{3})$

Step 2.2

Multiply $7$ by $2$ .

$14 \sqrt{3}$

$14 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt{3}$

Decimal Form:

$24.24871130 \dots$

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