Let X and Y axes be on the plane of the ring and Z be perpendicular to the ring.

Consider a small arc on the ring that makes an angle of  with the X axis and subtebds an angle of d at the ring's center. Then the electric field due to this element at a point located at a diatance on the Z axis is

Integrate the equation from 0 to 2 to get the answer

Finally as its given x << R, apply binomial approximation