Program To Evaluate Square Root Of A Number

Program To Evaluate Square Root Of A Number :-
#include<stdio.h>
#include<conio.h>
void main()
{
float a,q,b,i;
clrscr();
printf("Enter Any Number : ");
scanf("%f",&q);
a=b=q/2;
for(i=0;i<50;i++)
{
b=((a+(q/b))/2);
a=b;
}
printf("The Square Root Of %f Is -> %f",q,b);
getch();
}
                             THIS EVALUATION  IS BASED ON BABYLONIAN METHOD
Square roots by Divide-and-Average
This method dating back to the Babylonians (1700 B.C.) is known as the Babylonian Algorithm.
If A > 0 is a guess of the square root of the positive number Q, then a better approximation to √Q is given by
B = (A + Q/A)/2.
Now you use B as an approximation and compute C = (B + Q/B)/2, and so on to get as close as you want to the value of √Q. We have shown elsewhere why the Babylonian Algorithm works.
Example:
Let us find the square root of 5. Let A = 2.
Then B = (2 + 5/2)/2 = 2.25
C = (B + Q/B)/2 = (2.25 + 5/2.25)/2 = (2.25 + 2.22)/2 = 2.235
Notice that this value is getting closer with each iteration to the actual value 2.2360679...
You might wonder how one might even think of Q/A in connection with finding the square root of Q. Well, if A were indeed the square root of Q, then A2 = Q and so A = Q/A. And even if A is not the square root of Q so that A ¹ Q/A, it turns out that √Q lies strictly between A and Q/A, and their average B produces a shorter interval from B to Q/B within which √Q still lies and the average of B and Q/B produces an even shorter interval containing √Q, and so on.
FOR MORE GOTO http://en.wikipedia.org/wiki/Methods_of_computing_square_roots 
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Location: Pandeypur, Uttar Pradesh, India

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