Consider any infinitesimal charge element $dq$ on the ring. The distance from this element to the point on the axis is constant for all elements on the ring. This distance $r$ can be found using the Pythagorean theorem:

$$r = \sqrt{R^2 + x^2}$$

The potential $dU$ from the element $dq$ is $dU = k\frac{dq}{r}$. Since $r$ is constant, the total potential $U$ is found by summing the contributions from all charge elements:

$$U = \int dU = \int \frac{k dq}{r} = \frac{k}{r} \int dq$$

The integral of $dq$ over the entire ring is the total charge $q$.

$$U = \frac{kq}{r} = \frac{kq}{\sqrt{R^2 + x^2}}$$