Calculate error propagation from two dataset arrays

I want to calculate the error propagation from two different datasates.

F1=(a1, a2, a3,.....an)

F2=(b1, b2, b3,.....bn)

The error propagation wanted is gonna be like that dF = sqrt(dF1 + dF2) while the dF is the error propagation.

Please not I dont have the uncertainty on every value (a1,b2,....)