Integer square root in python

Note: There is now math.isqrt in stdlib, available since Python 3.8.

Newton’s method works perfectly well on integers:

def isqrt(n):
    x = n
    y = (x + 1) // 2
    while y < x:
        x = y
        y = (x + n // x) // 2
    return x

This returns the largest integer x for which x * x does not exceed n. If you want to check if the result is exactly the square root, simply perform the multiplication to check if n is a perfect square.

I discuss this algorithm, and three other algorithms for calculating square roots, at my blog.