平方根

def my_square(n):
	x = 1.0
	while 1:
		if x * x >= n:
			x=(x * x + (x - 1) * (x - 1)) / 2
			for i in range(0,10):
				j = n / x
				x = (j + x) / 2
			print '%.30f' % x
			break
		else:
			x = x + 1

↑小数点下30桁まで計算できる

↓誤差が出ないバージョン。小数点以下100桁まで。

UNTIL = 100

def f(n):
    xn = 0
    while xn * xn < n:
        xn += 1
    return len(str(xn))

def g(s, p):
    return s[:p] + '.' + s[p:]

def sq(n):
    a, b = 5*n, 5
    res = ''
    sz = 0
    cnt = 0
    while sz <= UNTIL:
        if a >= b:
            a, b = a-b, b+10
            cnt += 1
        else:
            a, b = a*100, (b/10)*100 + b%10
            res += str(cnt)
            sz += 1
            cnt = 0
    return g(res, f(n))

print sq(2)
print sq(10000)

# 初心者が書いたもの

# coding:utf-8

c = raw_input( "平方根を求めたい数値を入力:  " )
x = int( c )
a = float(0)
t = 1
n = 0
while t > a:
	 k = float(10**n)
	 n += 1
	 while a**2 > x:
		 a = a - 1/k
	 while a**2 < x:
		 a = a +1/k
	 t = a + 1
	 print "+-" + str(a)
	 if a**2 == x:
		 break

↓分数を使ったもの

#!/usr/bin/python
# -*- coding: utf-8 -*-
from fractions import Fraction
from decimal import Decimal, getcontext
from operator import truediv
from functools import reduce

getcontext().prec = 50
ZERO = Fraction('0/1')
ONE = Fraction('1/1')
HALF = Fraction('1/2')

def my_sqrt(num):
    '''
    ニュートン法で平方根を求める。
    '''
    if not 0 < num <= 10000:
        return 'Not implemented...'
    p = Fraction(num).limit_denominator()
    x0 = ZERO
    x1 = HALF * (ONE + p)
    for _ in range(12):
        x0 = x1
        x1 = HALF * (x0 + p / x0)
    x = str(x1)
    if '/' in x:
        return reduce(truediv, map(Decimal, x.split('/')))
    else:
        return '{0:30}'.format(x)

print(my_sqrt(0))
print(my_sqrt(1))
print(my_sqrt(2))
print(my_sqrt(3))
print(my_sqrt(10))
print(my_sqrt(100))
print(my_sqrt(0.0001))
print(my_sqrt(10000))