Trigonometry Examples

$\sqrt{\frac{357}{2} \cdot ((\frac{357}{2} - 71) (\frac{357}{2} - 119) (\frac{357}{2} - 167))}$

Step 1

To write $- 71$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{357}{2} \cdot (\frac{357}{2} - 71 \cdot \frac{2}{2}) (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 2

Combine $- 71$ and $\frac{2}{2}$ .

$\sqrt{\frac{357}{2} \cdot (\frac{357}{2} + \frac{- 71 \cdot 2}{2}) (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{357}{2} \cdot \frac{357 - 71 \cdot 2}{2} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 71$ by $2$ .

$\sqrt{\frac{357}{2} \cdot \frac{357 - 142}{2} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 4.2

Subtract $142$ from $357$ .

$\sqrt{\frac{357}{2} \cdot \frac{215}{2} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 5

Combine exponents.

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Step 5.1

Multiply $\frac{357}{2}$ by $\frac{215}{2}$ .

$\sqrt{\frac{357 \cdot 215}{2 \cdot 2} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 5.2

Multiply $357$ by $215$ .

$\sqrt{\frac{76755}{2 \cdot 2} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 5.3

Multiply $2$ by $2$ .

$\sqrt{\frac{76755}{4} (\frac{357}{2} - 119) (\frac{357}{2} - 167)}$

Step 6

To write $- 119$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{76755}{4} (\frac{357}{2} - 119 \cdot \frac{2}{2}) (\frac{357}{2} - 167)}$

Step 7

Combine $- 119$ and $\frac{2}{2}$ .

$\sqrt{\frac{76755}{4} (\frac{357}{2} + \frac{- 119 \cdot 2}{2}) (\frac{357}{2} - 167)}$

Step 8

Combine the numerators over the common denominator.

$\sqrt{\frac{76755}{4} \cdot \frac{357 - 119 \cdot 2}{2} (\frac{357}{2} - 167)}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 119$ by $2$ .

$\sqrt{\frac{76755}{4} \cdot \frac{357 - 238}{2} (\frac{357}{2} - 167)}$

Step 9.2

Subtract $238$ from $357$ .

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} (\frac{357}{2} - 167)}$

Step 10

To write $- 167$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} (\frac{357}{2} - 167 \cdot \frac{2}{2})}$

Step 11

Combine $- 167$ and $\frac{2}{2}$ .

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} (\frac{357}{2} + \frac{- 167 \cdot 2}{2})}$

Step 12

Combine the numerators over the common denominator.

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} \frac{357 - 167 \cdot 2}{2}}$

Step 13

Simplify the numerator.

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Step 13.1

Multiply $- 167$ by $2$ .

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} \frac{357 - 334}{2}}$

Step 13.2

Subtract $334$ from $357$ .

$\sqrt{\frac{76755}{4} \cdot \frac{119}{2} \frac{23}{2}}$

Step 14

Combine exponents.

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Step 14.1

Multiply $\frac{76755}{4}$ by $\frac{119}{2}$ .

$\sqrt{\frac{76755 \cdot 119}{4 \cdot 2} \cdot \frac{23}{2}}$

Step 14.2

Multiply $76755$ by $119$ .

$\sqrt{\frac{9133845}{4 \cdot 2} \cdot \frac{23}{2}}$

Step 14.3

Multiply $4$ by $2$ .

$\sqrt{\frac{9133845}{8} \cdot \frac{23}{2}}$

Step 14.4

Multiply $\frac{9133845}{8}$ by $\frac{23}{2}$ .

$\sqrt{\frac{9133845 \cdot 23}{8 \cdot 2}}$

Step 14.5

Multiply $9133845$ by $23$ .

$\sqrt{\frac{210078435}{8 \cdot 2}}$

Step 14.6

Multiply $8$ by $2$ .

$\sqrt{\frac{210078435}{16}}$

Step 15

Rewrite $\sqrt{\frac{210078435}{16}}$ as $\frac{\sqrt{210078435}}{\sqrt{16}}$ .

$\frac{\sqrt{210078435}}{\sqrt{16}}$

Step 16

Simplify the numerator.

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Step 16.1

Rewrite $210078435$ as $119^{2} \cdot 14835$ .

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Step 16.1.1

Factor $14161$ out of $210078435$ .

$\frac{\sqrt{14161 (14835)}}{\sqrt{16}}$

Step 16.1.2

Rewrite $14161$ as $119^{2}$ .

$\frac{\sqrt{119^{2} \cdot 14835}}{\sqrt{16}}$

Step 16.2

Pull terms out from under the radical.

$\frac{119 \sqrt{14835}}{\sqrt{16}}$

Step 17

Simplify the denominator.

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Step 17.1

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

$\frac{119 \sqrt{14835}}{\sqrt{4^{2}}}$

Step 17.2

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

$\frac{119 \sqrt{14835}}{4}$

Step 18

The result can be shown in multiple forms.

Exact Form:

$\frac{119 \sqrt{14835}}{4}$

Decimal Form:

$3623.52068953 \dots$