Algebra Examples

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

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 $27$ .

$- 3 \sqrt{9 (3)} - 3 \sqrt{27} - 3 \sqrt{27}$

Step 1.1.2

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

$- 3 \sqrt{3^{2} \cdot 3} - 3 \sqrt{27} - 3 \sqrt{27}$

Step 1.2

Pull terms out from under the radical.

$- 3 (| 3 | \sqrt{3}) - 3 \sqrt{27} - 3 \sqrt{27}$

Step 1.3

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

$- 3 (3 \sqrt{3}) - 3 \sqrt{27} - 3 \sqrt{27}$

Step 1.4

Multiply $3$ by $- 3$ .

$- 9 \sqrt{3} - 3 \sqrt{27} - 3 \sqrt{27}$

Step 1.5

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

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Step 1.5.1

Factor $9$ out of $27$ .

$- 9 \sqrt{3} - 3 \sqrt{9 (3)} - 3 \sqrt{27}$

Step 1.5.2

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

$- 9 \sqrt{3} - 3 \sqrt{3^{2} \cdot 3} - 3 \sqrt{27}$

Step 1.6

Pull terms out from under the radical.

$- 9 \sqrt{3} - 3 (| 3 | \sqrt{3}) - 3 \sqrt{27}$

Step 1.7

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

$- 9 \sqrt{3} - 3 (3 \sqrt{3}) - 3 \sqrt{27}$

Step 1.8

Multiply $3$ by $- 3$ .

$- 9 \sqrt{3} - 9 \sqrt{3} - 3 \sqrt{27}$

Step 1.9

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

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Step 1.9.1

Factor $9$ out of $27$ .

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

Step 1.9.2

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

$- 9 \sqrt{3} - 9 \sqrt{3} - 3 \sqrt{3^{2} \cdot 3}$

Step 1.10

Pull terms out from under the radical.

$- 9 \sqrt{3} - 9 \sqrt{3} - 3 (| 3 | \sqrt{3})$

Step 1.11

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

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

Step 1.12

Multiply $3$ by $- 3$ .

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

Step 2

Subtract $9 \sqrt{3}$ from $- 9 \sqrt{3}$ .

$- 18 \sqrt{3} - 9 \sqrt{3}$

Step 3

Subtract $9 \sqrt{3}$ from $- 18 \sqrt{3}$ .

$- 27 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 27 \sqrt{3}$

Decimal Form:

$- 46.76537180 \dots$