Rationalize the denominator of \(\dfrac{2}{\sqrt[3]{2} + \sqrt[3]{16}}\). The answer can be written in the form of A^(1/3)/B, where A and B are positive integers. Find the minimum possible value of A + B.
Note that ∛16 = ∛2^4 = 2 ∛2
So....the denominator just becomes
∛2 + 2∛2 = 3∛2
So we have
2
___ multiply num / den by 2^(2/3) = ∛(2^2) = ∛4
3∛2
2 * ∛ 4 2 * ∛4 2 * ∛4 ∛4 4^(1/3) / 3
_______ = _______ = _______ = _____ =
3∛2 * ∛4 3 * ∛8 3 * 2 3
A + B = 4 + 3 = 7
