from scipy.optimize import bisect
from scipy.optimize import newton
TOL = 1.e-4

def gg(z):
    return z**5 - 3.

z = bisect(gg, 0., 4., xtol=TOL)
z = newton(gg, z)

z0 = 3**0.2
print('z =', z, ' gg =', gg(z), ' error =', (z-z0)/z0)