How to handle units of measurement?

I'm trying to understand how Mathematica handles units of measurement.That is I expect that a calculation should return a certain unit, but I don't succeed. Let's consider this example:

(314.159 m Sqrt[((7.34102*10^-6 - 0.0000178801 I) s^2)/m^2])/s

The results should be a scalar to which I can apply Coth[] but I am unable to "convince" Mathematica to give me that.