Approximate a cube root with a binomial series

(i) Expand $\sqrt[3]{8+x}$ through $x^2$ and state the range of validity.

(ii) Put $x=1/27$ to approximate $\sqrt[3]{217}$ as $p/q$ in lowest terms, with $p,q\in\mathbb Z^+$.

(iii) We can also substitute $x=1/217$ into the expansion found in (i) to get an approximate value of $\sqrt[3]{217}$. Explain whether this approximation is better than the approximation in (ii).