Trigonometry Examples

$\sqrt{\frac{17}{2} \cdot ((\frac{17}{2} - 8) (\frac{17}{2} - 5) (\frac{17}{2} - 4))}$

Step 1

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{17}{2} \cdot (\frac{17}{2} - 8 \cdot \frac{2}{2}) (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 2

Combine $- 8$ and $\frac{2}{2}$ .

$\sqrt{\frac{17}{2} \cdot (\frac{17}{2} + \frac{- 8 \cdot 2}{2}) (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{17}{2} \cdot \frac{17 - 8 \cdot 2}{2} (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 8$ by $2$ .

$\sqrt{\frac{17}{2} \cdot \frac{17 - 16}{2} (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 4.2

Subtract $16$ from $17$ .

$\sqrt{\frac{17}{2} \cdot \frac{1}{2} (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 5

Combine exponents.

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Step 5.1

Multiply $\frac{17}{2}$ by $\frac{1}{2}$ .

$\sqrt{\frac{17}{2 \cdot 2} (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 5.2

Multiply $2$ by $2$ .

$\sqrt{\frac{17}{4} (\frac{17}{2} - 5) (\frac{17}{2} - 4)}$

Step 6

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{17}{4} (\frac{17}{2} - 5 \cdot \frac{2}{2}) (\frac{17}{2} - 4)}$

Step 7

Combine $- 5$ and $\frac{2}{2}$ .

$\sqrt{\frac{17}{4} (\frac{17}{2} + \frac{- 5 \cdot 2}{2}) (\frac{17}{2} - 4)}$

Step 8

Combine the numerators over the common denominator.

$\sqrt{\frac{17}{4} \cdot \frac{17 - 5 \cdot 2}{2} (\frac{17}{2} - 4)}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 5$ by $2$ .

$\sqrt{\frac{17}{4} \cdot \frac{17 - 10}{2} (\frac{17}{2} - 4)}$

Step 9.2

Subtract $10$ from $17$ .

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} (\frac{17}{2} - 4)}$

Step 10

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} (\frac{17}{2} - 4 \cdot \frac{2}{2})}$

Step 11

Combine $- 4$ and $\frac{2}{2}$ .

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} (\frac{17}{2} + \frac{- 4 \cdot 2}{2})}$

Step 12

Combine the numerators over the common denominator.

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} \frac{17 - 4 \cdot 2}{2}}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $- 4$ by $2$ .

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} \frac{17 - 8}{2}}$

Step 13.2

Subtract $8$ from $17$ .

$\sqrt{\frac{17}{4} \cdot \frac{7}{2} \frac{9}{2}}$

Step 14

Combine exponents.

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Step 14.1

Multiply $\frac{17}{4}$ by $\frac{7}{2}$ .

$\sqrt{\frac{17 \cdot 7}{4 \cdot 2} \cdot \frac{9}{2}}$

Step 14.2

Multiply $17$ by $7$ .

$\sqrt{\frac{119}{4 \cdot 2} \cdot \frac{9}{2}}$

Step 14.3

Multiply $4$ by $2$ .

$\sqrt{\frac{119}{8} \cdot \frac{9}{2}}$

Step 14.4

Multiply $\frac{119}{8}$ by $\frac{9}{2}$ .

$\sqrt{\frac{119 \cdot 9}{8 \cdot 2}}$

Step 14.5

Multiply $119$ by $9$ .

$\sqrt{\frac{1071}{8 \cdot 2}}$

Step 14.6

Multiply $8$ by $2$ .

$\sqrt{\frac{1071}{16}}$

Step 15

Rewrite $\sqrt{\frac{1071}{16}}$ as $\frac{\sqrt{1071}}{\sqrt{16}}$ .

$\frac{\sqrt{1071}}{\sqrt{16}}$

Step 16

Simplify the numerator.

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Step 16.1

Rewrite $1071$ as $3^{2} \cdot 119$ .

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Step 16.1.1

Factor $9$ out of $1071$ .

$\frac{\sqrt{9 (119)}}{\sqrt{16}}$

Step 16.1.2

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

$\frac{\sqrt{3^{2} \cdot 119}}{\sqrt{16}}$

Step 16.2

Pull terms out from under the radical.

$\frac{3 \sqrt{119}}{\sqrt{16}}$

Step 17

Simplify the denominator.

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Step 17.1

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

$\frac{3 \sqrt{119}}{\sqrt{4^{2}}}$

Step 17.2

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

$\frac{3 \sqrt{119}}{4}$

Step 18

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{119}}{4}$

Decimal Form:

$8.18153408 \dots$