Addition of numbers with same base but different exponents

Question

The problem itself is $(288\sqrt{3})^{1/5}+(288\sqrt{3})^{4/5}$. The answer is supposed to be of the form $a+b\sqrt{c}$, but I have no idea how to simplify it.

Answer 1

HINT: Note that $288\sqrt3=2^5\cdot3^{5/2}$, so the first term is simply $2\sqrt3$. Now what’s the second term?