Newton's method

#!/usr/bin/python3
def nsolve(n, a):
    e = 1e-16
    x = float(a)
    while True:
        x2 = x - (x**n - a) / (n * x**(n - 1))
        if abs(x2 - x) < e:
            break
        x = x2
    return x


for n, a in [(2, 5), (4, 2)]:
    x = nsolve(n, a)
    print(f'x**{n} = {a}, x = {x}')