Algebra Examples

$- 3 \sqrt{12} + 3 \sqrt{3} + 3 \sqrt{20}$

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 $12$ .

$- 3 \sqrt{4 (3)} + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1.1.2

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

$- 3 \sqrt{2^{2} \cdot 3} + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1.2

Pull terms out from under the radical.

$- 3 (| 2 | \sqrt{3}) + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 3 (2 \sqrt{3}) + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1.4

Multiply $2$ by $- 3$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1.5

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

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Step 1.5.1

Factor $4$ out of $20$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{4 (5)}$

Step 1.5.2

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

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{2^{2} \cdot 5}$

Step 1.6

Pull terms out from under the radical.

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 (| 2 | \sqrt{5})$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 (2 \sqrt{5})$

Step 1.8

Multiply $2$ by $3$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 6 \sqrt{5}$

Step 2

Add $- 6 \sqrt{3}$ and $3 \sqrt{3}$ .

$- 3 \sqrt{3} + 6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{3} + 6 \sqrt{5}$

Decimal Form:

$8.22025544 \dots$