The norms of the Bethe Ansatz eigenfunctions for the Lieb-Liniger quantum system of n Bosonic particles on a ring with pairwise repulsive delta potential interactions are given by a beautiful determinantal formula, first conjectured by Gaudin in the early seventies and then proven by Korepin about a decade later. Recently, E Emsiz formulated a similar conjecture generalizing the Gaudin-Korepin norm formula in terms of the root systems of complex simple Lie algebras. Here we confirm the validity of the conjecture in question for small root systems up to rank 3 ( thus including the important test case of the exceptional root system G(2)).