The commutator [x,d/dx] has to act on a function f(x). Then . So [x,d/dx] is actually the negative of the identity operator: it takes the function f(x) to –f(x).
The commutator [√,^2] has to act on a nonnegative real number. You should be able to work out for yourself that this is the zero operator: it takes each number to 0.