  In the recent paper, R. E. Curto, S. H. Lee, J. Yoon, asked the following
question: Let $A$ be a subnormal operator, and assume that $A^2$ is
quasinormal. Does it follow that $A$ is quasinormal? In this paper, we give an
affirmative answer to this question. In fact, we prove more general result that
subnormal $n$th roots of quasinormal operators are quasinormal.
