Question

Write a program that takes as input a positive real number s and a positive real number E and outputs the approximate value of Vs to within the tolerance E. In other words, the output of your program should be a number s' such that Is SIS E. (Thus the distance" between the output s' and the correct answer Vs should be at most E.) Your program should implement a very old algorithm for approximating the square root of numbers, called the Babylonian Method (also attributed to the Greek mathematician Hero of Alexandria and therefore sometimes called Hero's Method). Here is the pseudocode for this algorithm. 1. start with an arbitrary initial guess ao 0 and let i 1. 2. compute as the average of i-1 and s i-1 3. if the difference between ai and ai-1 is less than E, output zi and halt. 4. else increment i and return to step (2).

Answer 1

#include<stdio.h>
int main()
{
   float s,e,x1=1,x2=0;
   printf("Enter value of s : ");
   scanf("%f",&s);
   printf("Enter the value of e : ");
   scanf("%f",&e);
   while(1)
   {
       x2 = (x1 + s/(x1))/2;
       if(fabs(x2-x1)<=e)
       break;
       else
       x1=x2;
   }
   printf("approximate value of sqrt(%.0f) is : %f ",s,x2);
}

Answer 2

C Program Code:

#include<stdio.h>
//Function defintion
float squareRoot(float num)
{
float x = num;
float y = 1;
float e = 0.0001;
while(x - y > e)
{
   x = (x + y)/2;
    y = num/x;
}
return x;
}

//main method
int main()
{
int s;
printf("Enter value of s : ");
scanf("%f",&s);
printf ("Square root:%f", squareRoot(s));

}

Output: