A bounded linear operator $A$ on a Hilbert space $H$ is called a positive operator if $\langle Ax, x\rangle \geq 0$ for all  $x$ in $H$. It is known that, if $A$ is a positive operator on a Hilbert space  $H$ over the complex field $\mathbb{C}$, then $A$ has unique positive square root.
 
My question is the following: 
Does a normal positive operator on an infinite dimensional Hilbert space over the real field $\mathbb{R}$ ha*ve* a normal positive square root? If it exists, is it unique?