Trigonometry Examples

$\sqrt{\frac{1}{\frac{5}{\frac{16}{20}}}}$

Step 1

Cancel the common factor of $16$ and $20$ .

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Step 1.1

Factor $4$ out of $16$ .

$\sqrt{\frac{1}{\frac{5}{\frac{4 (4)}{20}}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $20$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $\frac{\frac{4}{5}}{5}$ by $1$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Multiply $\frac{4}{5} \cdot \frac{1}{5}$ .

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Step 5.1

Multiply $\frac{4}{5}$ by $\frac{1}{5}$ .

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

Step 5.2

Multiply $5$ by $5$ .

$\sqrt{\frac{4}{25}}$

Step 6

Rewrite $\sqrt{\frac{4}{25}}$ as $\frac{\sqrt{4}}{\sqrt{25}}$ .

$\frac{\sqrt{4}}{\sqrt{25}}$

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{\sqrt{2^{2}}}{\sqrt{25}}$

Step 7.2

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

$\frac{2}{\sqrt{25}}$

Step 8

Simplify the denominator.

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Step 8.1

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

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

Step 8.2

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

$\frac{2}{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$