Evaluate square root of 25/81

$\sqrt{\frac{25}{81}}$

Step 1

Rewrite $\sqrt{\frac{25}{81}}$ as $\frac{\sqrt{25}}{\sqrt{81}}$ .

$\frac{\sqrt{25}}{\sqrt{81}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt{5^{2}}}{\sqrt{81}}$

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

$\frac{5}{\sqrt{81}}$

Step 3

Simplify the denominator.

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

$\frac{5}{\sqrt{9^{2}}}$

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

$\frac{5}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{9}$

Decimal Form:

$0.\overline{5}$