Either
Reduce[-Sqrt[r] >= 0]
or
Simplify[-Sqrt[r] >= 0, r \[Element] Reals, TransformationFunctions -> {Automatic, Reduce}]
will produce
r == 0
The transformations available to Simplify and FullSimplify are limited to some extent. See the documentation of FullSimplify for a fuller example of using Reduce as a transformation function.
