Trigonometry Examples

$\sqrt{\frac{\frac{18}{13}}{\frac{8}{13}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{18}{13} \cdot \frac{13}{8}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $18$ .

$\sqrt{\frac{2 (9)}{13} \cdot \frac{13}{8}}$

Step 2.2

Factor $2$ out of $8$ .

$\sqrt{\frac{2 \cdot 9}{13} \cdot \frac{13}{2 \cdot 4}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9}{13} \cdot \frac{13}{2 \cdot 4}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9}{13} \cdot \frac{13}{4}}$

Step 3

Cancel the common factor of $13$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{9}{13} \cdot \frac{13}{4}}$

Step 3.2

Rewrite the expression.

$\sqrt{9 (\frac{1}{4})}$

Step 4

Combine $9$ and $\frac{1}{4}$ .

$\sqrt{\frac{9}{4}}$

Step 5

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

$\frac{\sqrt{9}}{\sqrt{4}}$

Step 6

Simplify the numerator.

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Step 6.1

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

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

Step 6.2

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

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

Step 7

Simplify the denominator.

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Step 7.1

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

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

Step 7.2

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

$\frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$