Basic Math Examples

$| 2 \sqrt{3} - 4 | - 3 \sqrt{12} + \sqrt{48} + 3$

Step 1

Simplify each term.

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Step 1.1

$2 \sqrt{3} - 4$ is approximately $- 0.53589838$ which is negative so negate $2 \sqrt{3} - 4$ and remove the absolute value

$- (2 \sqrt{3} - 4) - 3 \sqrt{12} + \sqrt{48} + 3$

Step 1.2

Apply the distributive property.

$- (2 \sqrt{3}) - - 4 - 3 \sqrt{12} + \sqrt{48} + 3$

Step 1.3

Multiply $2$ by $- 1$ .

$- 2 \sqrt{3} - - 4 - 3 \sqrt{12} + \sqrt{48} + 3$

Step 1.4

Multiply $- 1$ by $- 4$ .

$- 2 \sqrt{3} + 4 - 3 \sqrt{12} + \sqrt{48} + 3$

Step 1.5

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

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Step 1.5.1

Factor $4$ out of $12$ .

$- 2 \sqrt{3} + 4 - 3 \sqrt{4 (3)} + \sqrt{48} + 3$

Step 1.5.2

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

$- 2 \sqrt{3} + 4 - 3 \sqrt{2^{2} \cdot 3} + \sqrt{48} + 3$

Step 1.6

Pull terms out from under the radical.

$- 2 \sqrt{3} + 4 - 3 (2 \sqrt{3}) + \sqrt{48} + 3$

Step 1.7

Multiply $2$ by $- 3$ .

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + \sqrt{48} + 3$

Step 1.8

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

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Step 1.8.1

Factor $16$ out of $48$ .

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + \sqrt{16 (3)} + 3$

Step 1.8.2

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

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + \sqrt{4^{2} \cdot 3} + 3$

Step 1.9

Pull terms out from under the radical.

$- 2 \sqrt{3} + 4 - 6 \sqrt{3} + 4 \sqrt{3} + 3$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 \sqrt{3}$ from $- 2 \sqrt{3}$ .

$4 - 8 \sqrt{3} + 4 \sqrt{3} + 3$

Step 2.2

Add $4$ and $3$ .

$7 - 8 \sqrt{3} + 4 \sqrt{3}$

Step 2.3

Add $- 8 \sqrt{3}$ and $4 \sqrt{3}$ .

$7 - 4 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 - 4 \sqrt{3}$

Decimal Form:

$0.07179676 \dots$