An Iterative Method for Approximating Square Roots

Abstract

Introduction Mathematicians have been approximating the square roots of nonsquare integers with rational numbers for thousands of years. Many ingenious schemes have been used to generate these approximations and a good deal of interesting number theory has been discovered in the process. After reviewing some of these historical attempts and some of the number theory involved, we present an iterative procedure for approximating square roots which is based on an observation of M. A. Grant [3].