title: Finding the square root using Newton's method (errors!)
body: <p>I'm working to finish a math problem that approximates the square root of a number using Newton's guess and check method in Python. The user is supposed to enter a number, an initial guess for the number, and how many times they want to check their answer before returning. To make things easier and get to know Python (I've only just started learning the language a couple of months ago) I broke it up into a number of smaller functions; the problem now, though, is that I'm having trouble calling each function and passing the numbers through. </p>
  
  <p>Here is my code, with comments to help (each function is in order of use):</p>
  
  <pre><code># This program approximates the square root of a number (entered by the user)
  # using Newton's method (guess-and-check). I started with one long function,
  # but after research, have attempted to apply smaller functions on top of each
  # other.
  # * NEED TO: call functions properly; implement a counting loop so the
  # goodGuess function can only be accessed the certain # of times the user
  # specifies. Even if the - .001 range isn't reached, it should return.
  
  # sqrtNewt is basically the main, which initiates user input.
  
  def sqrtNewt():
      # c equals a running count initiated at the beginning of the program, to
      # use variable count.
      print("This will approximate the square root of a number, using a guess-and-check process.")
      x = eval(input("Please type in a positive number to find the square root of: "))
      guess = eval(input("Please type in a guess for the square root of the number you entered: "))
      count = eval(input("Please enter how many times would you like this program to improve your initial guess: ")) 
      avg = average(guess, x)
      g, avg = improveG(guess, x)
      final = goodGuess(avg, x)
      guess = square_root(guess, x, count)
      compare(guess, x)
  
  
  # Average function is called; is the first step that gives an initial average,
  # which implements through smaller layers of simple functions stacked on each
  # other.
  def average(guess, x) :
      return ((guess + x) / 2)
  
  # An improvement function which builds upon the original average function.
  def improveG(guess, x) :
      return average(guess, x/guess)
  
  # A function which determines if the difference between guess X guess minus the
  # original number results in an absolute vale less than 0.001. Not taking
  # absolute values (like if guess times guess was greater than x) might result
  # in errors
  from math import *
  def goodGuess(avg, x) :
      num = abs(avg * avg - x)
      return (num &lt; 0.001)
  
  # A function that, if not satisfied, continues to "tap" other functions for
  # better guess outputs. i.e. as long as the guess is not good enough, keep
  # improving the guess.
  def square_root(guess, x, count) :
      while(not goodGuess(avg, x)):
          c = 0
          c = c + 1
          if (c &lt; count):
              guess = improveG(guess, x)
          elif (c == count):
              return guess
          else :
              pass
  
  # Function is used to check the difference between guess and the sqrt method
  # applied to the user input.
  import math
  def compare(guess, x):
      diff = math.sqrt(x) - guess
      print("The following is the difference between the approximation") 
      print("and the Math.sqrt method, not rounded:", diff)
  
  sqrtNewt()
  </code></pre>
  
  <p>Currently, I get this error: <code>g, avg = improveG(guess, x)
  TypeError: 'float' object is not iterable.</code>
  The final function uses the final iteration of the guess to subtract from the math square root method, and returns the overall difference.
  Am I even doing this right? Working code would be appreciated, with suggestions, if you can provide it. Again, I'm a newbie, so I apologize for misconceptions or blind obvious errors.</p>