I How to Estimate Uncertainty for a Physical Quantity with Dependent Variables?

[bznm]

I have a physical quantity A defined as $A=(74.5 B^2*(M+N))^{1/3}$

where B, M, N and relative uncertainties are given. And M and N are dependent on B.
Could you show me how to calculate and estimation for the uncertainty on A?

Thanks a lot

 

[Vanadium 50]

You will need to know the correlation between the uncertainties on M and N and the uncertainties on B. If you think this is small, you can treat them as independent.

 

[bznm]

M and N are function of B (ie for example $log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)$ The value of B is given by a software, and its uncertainty is 0.0002.
The values of M and N are extimated using relations like the one that I have just written, and it is assumed that the error is 15%.
How can I estimate the uncertainty on A?