  The primary purpose of this paper is to show the existence of normal square
and nth roots of some classes of bounded operators on Hilbert spaces. Two
interesting simple results hold. Namely, under simple conditions we show that
if any operator $T$ is such that $T^2=0$, then this implies that $T$ is normal
and so $T=0$. Also, we will see when the square root of an arbitrary bounded
operator is normal.
