Question:

Q1) Write a code that asks the user for a positive integer, computes the square root of that integer, and return the result to the user. The computational error needs to be smaller than 0.01.

1.      Get a positive integer 'X' as the input.

2.      Start from an initial guess, G.

3.      Compute the error = (G^2 - X).

4.      If error < 0.01, report the G as the result and stop. If not, go to 5.

5.      Update G, G = (G + X/G)/2. Go to 3.

Code Block

//This program computes the square root of a given positive integer and is written by Vahid D on 13/1/13

#include
   using namespace std;
   int main()
   {
      double G = 10, err; // G is an initial guess and err is the error
      int X; // input, positive integer
      cout << "Enter a positive integer: \n"; //ask user to enter a number
      cin >> X; // get the input
      
      err = (G*G - X); // compute the error
      while ( err > 0.01) // continue updating G till the error is smaller than 0.01
      {
          G   = (G + X/G)/2;
          err = (G*G - X);
      }
      
      cout << "Square root of " << X << " is: " << G << endl; // report the result
      return 0;
   }