  The paper provides a study of pseudo MV-algebras with square roots. We
introduce different notions of a square root on a pseudo MV-algebra, and
present their main properties. We show that the class of pseudo-MV-algebras
with square roots is a proper subvariety of the variety of pseudo MV-algebras.
Then, we define a strict square root to classify the class of pseudo
MV-algebras with square roots. We found a relationship between strongly
atomless pseudo MV-algebras and strict pseudo MV-algebras. Finally, we
investigate square roots on representable symmetric pseudo MV-algebras, and we
present a complete characterization of a square root and a weak square root on
a representable symmetric pseudo MV-algebra using addition in a unital
$\ell$-group. Some interesting examples are provided.
