Square Root Approximation with Binary Search-Like Method:

How many iterations will the following Java program perform before print

ing the approximated square root of 64, with an initial guess of n/2 and

a tolerance of 0.01? The method used is a binary search-like approach to

approximate the square root.

 double n = 64;

// Improved initial guess

 double guess = n / 2; // Better starting point 

 double tolerance = 0.01; 

 double low = 0;

 double high = n; 

 int iteration = 0; 

 // Binary search−like method for square root approximation 

 while (Math.abs(guess ∗ guess − n) > tolerance) {

 guess = (low + high) / 2; // Midpoint of range 

 if (guess ∗ guess < n) {  

low = guess; // Move lower bound up

 } 

else {  high = guess ; // Move upper bound down

 }

 i t eration++; 

 } 

 System. out . println (”Number of iterations : ” + iteration ); 

 System. out . println (”Approximated square root : ” + guess );

 } 

 }