Algebra Examples

$- 2 \sqrt{3} + 3 \sqrt{27}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $27$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Step 1.4

Multiply $3$ by $3$ .

$- 2 \sqrt{3} + 9 \sqrt{3}$

Step 2

Add $- 2 \sqrt{3}$ and $9 \sqrt{3}$ .

$7 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{3}$

Decimal Form:

$12.12435565 \dots$