Simplify square root of 1/81

$\sqrt{\frac{1}{81}}$

Rewrite $\sqrt{\frac{1}{81}}$ as $\frac{\sqrt{1}}{\sqrt{81}}$ .

$\frac{\sqrt{1}}{\sqrt{81}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{81}}$

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$\frac{1}{\sqrt{9^{2}}}$

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

$\frac{1}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$