Whether $A^{1/2} \ge B^{1/2}$ is true when $A$ and $B$ are unbounded operators on a Hilbert space

Question

Let $H$ be a Hilbert space and $B(H)$ be the set of all bounded linear operators on it. It is known that if $A,B\in B(H)$ and $A\ge B \ge 0$, then $A^{1/2} \ge B^{1/2}$ [Takesaki, Chapter 1, Proposition 6.3, Theory of operator algebra I, 1979]. I would like to ask whether it is still true when $A$ and $B$ are unbounded closed and densely defined operators.