[Tutor] newton's sqrt formula

[WM.]

# program to find square root
square = input ('Please enter a number to be rooted, ')
square = square * 1.0
guess = input('Please guess at the root, ')
guess = guess * 1.0
newguess = 0.

while guess**2 != square:
         # Newton's formula
         newguess = guess - (guess * guess - square) / (guess * 2)
         guess = newguess
         guess**2 - square
print
print
print guess, ' is the square root of ', square
print
print
print 'bye'
Last month there was a square root program discussed. I wondered if the 
tide of my ignorance had receded enough that I could take a whack at 
messing with it.
I offer this rewrite for your critique. Can it be terser, faster, prettier?
Thank you.