The present disclosure relates generally to the field of oral surgery and, more particularly, to a minimally invasive method of extracting fractured root tips of teeth from the corresponding tooth socket. In some embodiments, the method comprises the steps of selecting a broken root tip removal instrument which comprises a finger grip coupled to a conical radial tip comprising a spiral cutting screw and then placing the fine point against an exposed surface of a broken root tip, subsequently applying a torque to the finger grip thereby causing the radial tip to screw into the broken root tip such that the root tip removal instrument securely anchors into the broken root tip, and finally applying a force to the finger grip thereby extracting the broken root tip from a root canal.