Question

Find the rationalising factor of
5^(1/3) + 5^(-1/3)

Answer 1

5^(1/3) + 5^(-1/3)
= 5^(1/3) + 1 / 5^(1/3) * 5(2/3)/5^(2/3)
= 5(1/3) + 5^(2/3) / 5

hope this is what you meant, there is no longer any irrational
number in the denominator.

Answer 2

note that you can use the difference of cubes formula
x+y = (∛x + ∛y)(∛x^2 - ∛xy + ∛y^2)
so plug in x = 5 and y = 1/5