Pre-Algebra Examples

$- \frac{2 + \sqrt{108}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $108$ as $6^{2} \cdot 3$ .

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Step 1.1.1

Factor $36$ out of $108$ .

$- \frac{2 + \sqrt{36 (3)}}{2}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 2

Cancel the common factor of $2 + 6 \sqrt{3}$ and $2$ .

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Step 2.1

Factor $2$ out of $2$ .

$- \frac{2 \cdot 1 + 6 \sqrt{3}}{2}$

Step 2.2

Factor $2$ out of $6 \sqrt{3}$ .

$- \frac{2 \cdot 1 + 2 (3 \sqrt{3})}{2}$

Step 2.3

Factor $2$ out of $2 (1) + 2 (3 \sqrt{3})$ .

$- \frac{2 (1 + 3 \sqrt{3})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$- \frac{2 (1 + 3 \sqrt{3})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$- \frac{2 (1 + 3 \sqrt{3})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$- \frac{1 + 3 \sqrt{3}}{1}$

Step 2.4.4

Divide $1 + 3 \sqrt{3}$ by $1$ .

$- (1 + 3 \sqrt{3})$

$- (1 + 3 \sqrt{3})$

$- (1 + 3 \sqrt{3})$

Step 3

Apply the distributive property.

$- 1 \cdot 1 - (3 \sqrt{3})$

Step 4

Multiply $- 1$ by $1$ .

$- 1 - (3 \sqrt{3})$

Step 5

Multiply $3$ by $- 1$ .

$- 1 - 3 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 1 - 3 \sqrt{3}$

Decimal Form:

$- 6.19615242 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$