Evaluate square root of 18/121

$\sqrt{\frac{18}{121}}$

Rewrite $\sqrt{\frac{18}{121}}$ as $\frac{\sqrt{18}}{\sqrt{121}}$ .

$\frac{\sqrt{18}}{\sqrt{121}}$

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{\sqrt{9 (2)}}{\sqrt{121}}$

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

$\frac{\sqrt{3^{2} \cdot 2}}{\sqrt{121}}$

Pull terms out from under the radical.

$\frac{3 \sqrt{2}}{\sqrt{121}}$

Simplify the denominator.

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

$\frac{3 \sqrt{2}}{\sqrt{11^{2}}}$

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

$\frac{3 \sqrt{2}}{11}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{11}$

Decimal Form:

$0.38569460 \dots$