Latecoere:
eggs, there is no need in this example to talk about compressibility. Speed is less than 250 kt.
Actually the guy asked for an "exact" answer and a formula, so I gave the formula both with and without compressibility. And I also wrote
"compressibility is generally considered insignificant at the lowish speed and altitude in your example".
Regarding density of the air the most important to know>>> what does affect it :
-Pressure (Altitude)
-Temperature
-Humidity
I was answering the question the OP asked, as opposed to the question you think is more important
The formula is: TAS = CAS/√Relative Density.....the rule of thumb you gave is a useful approximation. We all use them. But it is an approximation and the OP asked for an "exact" TAS.