I need a way to approach this problem. I saw this problem in chapter 3, section 3.4 of numerical analysis. I appreciate any help on any idea that may help me start out with this problem.

Show that the following method has third order convergence for computing R^{1/2}

X_{n+1}= X_{n}(X^{2}_{n}+3R)/(3X^{2}_{n}+R)

Thank you.