2.7

The "divide and average" method, an old-time method for approximating the square root of any positive number a can be formulated as x=(x+a/x)/2.

For this problem, we wrote a function

function [ sqrroot ] = fp27( a )

tol = 1.0E-5;

if (a>0)

    

     x = a/2; 

    while(1==1)

      y = (x+a/x)/2;

      e = abs((y-x)/y);

      x=y;

      if (e<tol) break;

    end

    end

    

    sqrroot = x;

else

    sqrroot = 0;

end

end

which can be implemented for verification as follows

EDU>> fp27(4)

ans =

     2

EDU>> fp27(9)

ans =

    3.0000

EDU>> fp27(16)

ans =

    4.0000