For a graph G=(V,E), its exact-distance square, G[♯2], is the with vertex set V and an edge between vertices x y if only have distance (exactly) 2 in G. The G square root of G[♯2]. We give characterization graphs having root, our easily leading to polynomial-time recognition algorithm. show that it NP-complete recognize bipartite root. These two results strongly contrast known on (usual) square...