Evaluate square root of 25/121

$\sqrt{\frac{25}{121}}$

Step 1

Rewrite $\sqrt{\frac{25}{121}}$ as $\frac{\sqrt{25}}{\sqrt{121}}$ .

$\frac{\sqrt{25}}{\sqrt{121}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt{5^{2}}}{\sqrt{121}}$

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

$\frac{5}{\sqrt{121}}$

Step 3

Simplify the denominator.

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

$\frac{5}{\sqrt{11^{2}}}$

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

$\frac{5}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{11}$

Decimal Form:

$0.\overline{45}$