Answer:
This problem is providing the ionic radius of an anion, A²⁻ as 0.290 nm and asks for that of the cation A²⁺ in comparison to the former.
Firstly, we need to recall the concept of ionic radius, as the distance between the nucleus and the outermost electron shell of an ion. In such a way, we can have two scenarios:
1. Anions result from the gain of electrons exhibited by a nonmetal, which means they turn out bigger than the neutral atom.
2. Cations result from the loss of electrons exhibited by a metal, which means they turn out smaller than the neutral atom.
With the aforementioned, we infer that the cation A²⁺, will me smaller than the anion A²⁻, which means it will have an ionic radius smaller than 0.290 nm.