Trigonometry Examples

$\sqrt{\frac{\frac{1}{5}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{1}{5} \cdot \frac{1}{2}}$

Step 2

Multiply $\frac{1}{5} \cdot \frac{1}{2}$ .

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Step 2.1

Multiply $\frac{1}{5}$ by $\frac{1}{2}$ .

$\sqrt{\frac{1}{5 \cdot 2}}$

Step 2.2

Multiply $5$ by $2$ .

$\sqrt{\frac{1}{10}}$

Step 3

Rewrite $\sqrt{\frac{1}{10}}$ as $\frac{\sqrt{1}}{\sqrt{10}}$ .

$\frac{\sqrt{1}}{\sqrt{10}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{10}}$

Step 5

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{\sqrt{10} \sqrt{10}}$

Step 6.2

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Step 6.3

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\frac{\sqrt{10}}{{\sqrt{10}}^{2}}$

Step 6.6

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Step 6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$\frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$\frac{\sqrt{10}}{10^{1}}$

Step 6.6.5

Evaluate the exponent.

$\frac{\sqrt{10}}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{10}$

Decimal Form:

$0.31622776 \dots$