Answer the following:

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

Answer the following: (i) Evaluate

(125)^{\frac{2}{3}}

. (ii) Using your result from part (i), simplify

\displaystyle\frac{(125)^{\frac{2}{3}}}{2+\sqrt{5}}

so that the denominator is rational.