Show Newton's method for the square root of a is the average of guess and a/guess. That is, show that Newton's Method for finding the positive square root of a positive Note that: if our current guess, Xn, IS number, a, can be given by x+1 Xn+1 X too low then a/x, is too high and vice versa. So taking the average of the two should be an improvement. Show that Newton's method for x - a=0 can be written as 1 == 2 1 = x +- 2 a x + = X a