Trigonometry Examples

$\sqrt{\frac{1 - (- \frac{8}{17})}{1 - \frac{8}{17}}}$

Step 1

Multiply $- (- \frac{8}{17})$ .

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Step 1.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{8}{17})}{1 - \frac{8}{17}}}$

Step 1.2

Multiply $\frac{8}{17}$ by $1$ .

$\sqrt{\frac{1 + \frac{8}{17}}{1 - \frac{8}{17}}}$

Step 2

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{17}{17} + \frac{8}{17}}{1 - \frac{8}{17}}}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{17 + 8}{17}}{1 - \frac{8}{17}}}$

Step 4

Add $17$ and $8$ .

$\sqrt{\frac{\frac{25}{17}}{1 - \frac{8}{17}}}$

Step 5

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{25}{17}}{\frac{17}{17} - \frac{8}{17}}}$

Step 6

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{25}{17}}{\frac{17 - 8}{17}}}$

Step 7

Subtract $8$ from $17$ .

$\sqrt{\frac{\frac{25}{17}}{\frac{9}{17}}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{25}{17} \cdot \frac{17}{9}}$

Step 9

Cancel the common factor of $17$ .

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Step 9.1

Cancel the common factor.

$\sqrt{\frac{25}{17} \cdot \frac{17}{9}}$

Step 9.2

Rewrite the expression.

$\sqrt{25 (\frac{1}{9})}$

Step 10

Combine $25$ and $\frac{1}{9}$ .

$\sqrt{\frac{25}{9}}$

Step 11

Rewrite $\sqrt{\frac{25}{9}}$ as $\frac{\sqrt{25}}{\sqrt{9}}$ .

$\frac{\sqrt{25}}{\sqrt{9}}$

Step 12

Simplify the numerator.

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Step 12.1

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{5^{2}}}{\sqrt{9}}$

Step 12.2

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

$\frac{5}{\sqrt{9}}$

Step 13

Simplify the denominator.

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Step 13.1

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

$\frac{5}{\sqrt{3^{2}}}$

Step 13.2

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

$\frac{5}{3}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$