using System;

public class Program

{

    public static void Main()

    {

        double x = 1.953125;

        double y = .00002963125;

        https://www.wolframalpha.com/input/?i=sqrt%281.953125%5E2+%2B+.00002963125%5E2%29

        double correctAnswer = 1.9531250002247708099870663892423060726610677445818558359259;

        Console.WriteLine("Naive way: error = {0:G20}", Math.Sqrt(x*x + y*y) - correctAnswer);

        Console.WriteLine("Better way: error = {0:G20}", x * Math.Sqrt(1 + (y/x) * (y/x)) - correctAnswer);

    }

}