Thanks for your reply but the square is in the outermost bracket

The equation

It really comes down to what you would like to do with this later one. If the result is treated as a random variable, I would suggest the following:

1- Nt >> 1, assume the summation is a Gaussian RV (law of large numbers)

2- In general, approximate sum_i \sqrt{ e^{snr_i}} as max_i e^{snr_i}. The reason being that exp() is a steep function and if you sum of over all such terms, most probably one of them will be dominant.

Thanks for your answer