For any positive number a the problem of calculating the

Question

Question: For any positive number, a, the problem of calculating the square root, √a , is often done by applying Newton's method to the function f(x) = x²-a. Apply the method to obtain an expression for x_n+1 in terms of x_n. Use this to approximate √a for a = 2, 10, 1000, and π, correct to four decimal places, starting at x0 = a/2 in each case.