Agreed, it's all about making quick and accurate approximations. You ought to know the Taylor expansions for sinx, cosx, e^x as well as the binomial approximation. But really, most questions don't require that sort of math.
You should know how to estimate some common figures. For example, sqrt2 = 1.4, sqrt3=1.7, ln2 = 0.7.
The example given by throwaway, could be done like:
(7/5)^(2/3) = (49/25)^(1/3) = 2^(1/3) < 2^(1/2)
So 2^(1/3) < 1.4
Just do a bunch of practice problems, and it will become evident what sort of numerical approximations are expected. If a problem seems too mathematically technical, you've either missed the intended approach or are being far too accurate!