On the square root of languages

The unambiguous square root of a language L subset of or equal to Sigma* is a language X s.t. X-2 = L and the product is unambiguous. We prove that: 1. Every language admits at most one unambiguous square root 2. For the class of regular languages, it is decidable whether the unambiguous square root is regular; the same problem becomes undecidable for the class of context-free languages 3. The unambiguous square root of a language in P is in P.