I am asked to find $\sqrt{2012}$ using Newton-Raphson's Method with the following recursive method
$$x_{n+1} = \frac{1}{2} (x_n + \frac{a}{x_n}) $$
I notied that give same answers as using
$$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} $$
This is easy, but the next part asks to find a similar recursive method to find $\sqrt[3]{2012}$. How do I find such a method?
UPDATE
I did
$$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 12.7551$$
$$x_2 = 12.6257$$
$$x_3 = 12.6244$$
$$x_4 = 12.6244$$
$$x_4 ^ 3 = 2012.02$$
Which seems correct. But I didn't use a similar recursive method like the question asked?