Trigonometry Examples

$- \sqrt{1 {(- \frac{1}{5})}^{2}}$

Step 1

Multiply ${(- \frac{1}{5})}^{2}$ by $1$ .

$- \sqrt{{(- \frac{1}{5})}^{2}}$

Step 2

Apply the product rule to $- \frac{1}{5}$ .

$- \sqrt{{(- 1)}^{2} {(\frac{1}{5})}^{2}}$

Step 3

Raise $- 1$ to the power of $2$ .

$- \sqrt{1 {(\frac{1}{5})}^{2}}$

Step 4

Apply the product rule to $\frac{1}{5}$ .

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

Step 5

One to any power is one.

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

Step 6

Raise $5$ to the power of $2$ .

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

Step 7

Multiply $\frac{1}{25}$ by $1$ .

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

Step 8

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

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

Step 9

Any root of $1$ is $1$ .

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

Step 10

Simplify the denominator.

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Step 10.1

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

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

Step 10.2

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

$- \frac{1}{5}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{5}$

Decimal Form:

$- 0.2$