Algebra Examples

$- 9 \sqrt{3} - \sqrt{9} + \sqrt{48} + \sqrt{12}$

Step 1

Simplify each term.

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Step 1.1

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

$- 9 \sqrt{3} - \sqrt{3^{2}} + \sqrt{48} + \sqrt{12}$

Step 1.2

Pull terms out from under the radical.

$- 9 \sqrt{3} - | 3 | + \sqrt{48} + \sqrt{12}$

Step 1.3

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

$- 9 \sqrt{3} - 1 \cdot 3 + \sqrt{48} + \sqrt{12}$

Step 1.4

Multiply $- 1$ by $3$ .

$- 9 \sqrt{3} - 3 + \sqrt{48} + \sqrt{12}$

Step 1.5

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

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Step 1.5.1

Factor $16$ out of $48$ .

$- 9 \sqrt{3} - 3 + \sqrt{16 (3)} + \sqrt{12}$

Step 1.5.2

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

$- 9 \sqrt{3} - 3 + \sqrt{4^{2} \cdot 3} + \sqrt{12}$

Step 1.6

Pull terms out from under the radical.

$- 9 \sqrt{3} - 3 + | 4 | \sqrt{3} + \sqrt{12}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$- 9 \sqrt{3} - 3 + 4 \sqrt{3} + \sqrt{12}$

Step 1.8

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.8.1

Factor $4$ out of $12$ .

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

Step 1.8.2

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

$- 9 \sqrt{3} - 3 + 4 \sqrt{3} + \sqrt{2^{2} \cdot 3}$

Step 1.9

Pull terms out from under the radical.

$- 9 \sqrt{3} - 3 + 4 \sqrt{3} + | 2 | \sqrt{3}$

Step 1.10

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

$- 9 \sqrt{3} - 3 + 4 \sqrt{3} + 2 \sqrt{3}$

Step 2

Add $- 9 \sqrt{3}$ and $4 \sqrt{3}$ .

$- 3 - 5 \sqrt{3} + 2 \sqrt{3}$

Step 3

Add $- 5 \sqrt{3}$ and $2 \sqrt{3}$ .

$- 3 - 3 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 3 - 3 \sqrt{3}$

Decimal Form:

$- 8.19615242 \dots$