sqroot.py

n = 12427281805225 # 3525235

# brute force, ~.5s
for i in xrange(1, n):
    if i**2 == n:
        print i
        break

# binary search.. ~.06s
def find_sq_root(n, lower=1, upper=n):
    m = (lower + upper) / 2

    if m**2 == n:
        return m

    if m**2 > n:
        return find_sq_root(n, lower, m)
    else:
        return find_sq_root(n, m, upper)

print find_sq_root(n)