Evaluate - square root of 1/121

$- \sqrt{\frac{1}{121}}$

Step 1

Rewrite $\sqrt{\frac{1}{121}}$ as $\frac{\sqrt{1}}{\sqrt{121}}$ .

$- \frac{\sqrt{1}}{\sqrt{121}}$

Step 2

Any root of $1$ is $1$ .

$- \frac{1}{\sqrt{121}}$

Step 3

Simplify the denominator.

Rewrite $121$ as $11^{2}$ .

$- \frac{1}{\sqrt{11^{2}}}$

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

$- \frac{1}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{11}$

Decimal Form:

$- 0.\overline{09}$