Energy of a graph is never the square root of an odd integer

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. Bapat and Pati (Bull. Kerala Math. Assoc., 1 (2004) 129-132) proved that (a) E(G) is never an odd integer. We now show that (b) E(G) is never the square root of an odd integer. Furthermore, if r and s are integers such that r ≥ 1 and 0 ≤ s ≤ r - 1 and q is an odd integer, then E(G) cannot be of the form (2s q)1/r, a result that implies both (a) and (b) as special cases.