Trigonometry Examples

$\sqrt{\frac{\frac{2}{5}}{\frac{8}{5}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{2}{5} \cdot \frac{5}{8}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $8$ .

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

Step 2.2

Cancel the common factor.

$\sqrt{\frac{2}{5} \cdot \frac{5}{2 \cdot 4}}$

Step 2.3

Rewrite the expression.

$\sqrt{\frac{1}{5} \cdot \frac{5}{4}}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{1}{5} \cdot \frac{5}{4}}$

Step 3.2

Rewrite the expression.

$\sqrt{\frac{1}{4}}$

Step 4

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{\sqrt{1}}{\sqrt{4}}$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{4}}$

Step 6

Simplify the denominator.

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Step 6.1

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

$\frac{1}{\sqrt{2^{2}}}$

Step 6.2

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

$\frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$