Two ways of approximation of Pi and its square root

In this paper we discuss two methods of approximations of π and it's square root. The approximation of in the first method uses a unit circle and has been around for quite some time, but the part concerning approximation of is new. The second approximation makes use of the bell shaped curve y=e^−x2 and the error function. Both the approximations are based on the Monte Carlo Simulation Method. The method requires of picking points (called sample) at random and counting those that satisfy certain criteria. The number is called the sample size. Here we determine the minimum sample sizes required to obtain an approximation so that the absolute error is less than a given value.