Trigonometry Examples

$2 (- \frac{3}{11}) (\frac{- \sqrt{112}}{11})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 1.1.1

Factor $16$ out of $112$ .

$2 (- \frac{3}{11}) \cdot \frac{- \sqrt{16 (7)}}{11}$

Step 1.1.2

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

$2 (- \frac{3}{11}) \cdot \frac{- \sqrt{4^{2} \cdot 7}}{11}$

Step 1.2

Pull terms out from under the radical.

$2 (- \frac{3}{11}) \cdot \frac{- 1 \cdot 4 \sqrt{7}}{11}$

Step 1.3

Multiply $- 1$ by $4$ .

$2 (- \frac{3}{11}) \cdot \frac{- 4 \sqrt{7}}{11}$

Step 2

Multiply $2 (- \frac{3}{11})$ .

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Step 2.1

Multiply $- 1$ by $2$ .

$- 2 (\frac{3}{11}) \cdot \frac{- 4 \sqrt{7}}{11}$

Step 2.2

Combine $- 2$ and $\frac{3}{11}$ .

$\frac{- 2 \cdot 3}{11} \cdot \frac{- 4 \sqrt{7}}{11}$

Step 2.3

Multiply $- 2$ by $3$ .

$\frac{- 6}{11} \cdot \frac{- 4 \sqrt{7}}{11}$

Step 3

Move the negative in front of the fraction.

$- \frac{6}{11} \cdot \frac{- 4 \sqrt{7}}{11}$

Step 4

Move the negative in front of the fraction.

$- \frac{6}{11} \cdot (- \frac{4 \sqrt{7}}{11})$

Step 5

Multiply $- \frac{6}{11} (- \frac{4 \sqrt{7}}{11})$ .

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Step 5.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{6}{11}) \frac{4 \sqrt{7}}{11}$

Step 5.2

Multiply $\frac{6}{11}$ by $1$ .

$\frac{6}{11} \cdot \frac{4 \sqrt{7}}{11}$

Step 5.3

Multiply $\frac{6}{11}$ by $\frac{4 \sqrt{7}}{11}$ .

$\frac{6 (4 \sqrt{7})}{11 \cdot 11}$

Step 5.4

Multiply $4$ by $6$ .

$\frac{24 \sqrt{7}}{11 \cdot 11}$

Step 5.5

Multiply $11$ by $11$ .

$\frac{24 \sqrt{7}}{121}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{24 \sqrt{7}}{121}$

Decimal Form:

$0.52477711 \dots$