Find the Exact Value square root of 1/9

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

Step 1

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

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

Step 2

Any root of $1$ is $1$ .

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

Step 3

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\sqrt{3^{2}}}$

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

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$