  In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with
square roots. In the present paper, the main aim is to continue to study the
structure of pseudo MV-algebras with square roots focusing on their new
characterizations. The paper is divided into two parts. In the first part, we
investigate the relationship between a pseudo MV-algebra with square root and
its corresponding unital $\ell$-group in the scene of two-divisibility.
  In the present second part, we find some conditions under which a particular
class of pseudo MV-algebras can be embedded into pseudo MV-algebras with square
roots. We introduce and investigate the concepts of a strict square root of a
pseudo MV-algebra and a square root closure, and we compare both notions. We
show that each MV-algebra has a square root closure. Finally, using the square
root of individual elements of a pseudo MV-algebra, we find the greatest
subalgebra of a special pseudo MV-algebra with weak square root.
