def find_root(a, b, tol, f):
    """ a < b are real numbers, f is continous on [a,b]
    tol > 0 is an error tolerance
    postc: returns a number x within tol of the root of f on [a,b]"""
    while b - a > 2*tol:
        m = (a + b)/2
        if f(a)*f(m) < 0:
            b = m
        elif f(b)*f(m) < 0:
            a = m
    return m

print(find_root(1, 2, .0001, lambda x:x*x - 2))
print(2**(.5))
print(find_root(1,1000, .0001, lambda x: x**3 - 100))