Trigonometry Examples

$- \frac{\sqrt{108}}{2 \sqrt{3}}$

Step 1

Combine $\sqrt{108}$ and $\sqrt{3}$ into a single radical.

$- \frac{\sqrt{\frac{108}{3}}}{2}$

Step 2

Cancel the common factor of $108$ and $3$ .

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Step 2.1

Factor $3$ out of $108$ .

$- \frac{\sqrt{\frac{3 \cdot 36}{3}}}{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3$ .

$- \frac{\sqrt{\frac{3 \cdot 36}{3 (1)}}}{2}$

Step 2.2.2

Cancel the common factor.

$- \frac{\sqrt{\frac{3 \cdot 36}{3 \cdot 1}}}{2}$

Step 2.2.3

Rewrite the expression.

$- \frac{\sqrt{\frac{36}{1}}}{2}$

Step 2.2.4

Divide $36$ by $1$ .

$- \frac{\sqrt{36}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

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

$- \frac{\sqrt{6^{2}}}{2}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{6}{2}$

Step 4

Simplify the expression.

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Step 4.1

Divide $6$ by $2$ .

$- 1 \cdot 3$

Step 4.2

Multiply $- 1$ by $3$ .

$- 3$