It is correct.
a = a1, a2 = sqrt(10^-4), sqrt(1+10^-4) = 10^-2, 1 + O(10^-4)
b = sqrt(a1), sqrt(a2)
Sum b = sqrt(a1) + sqrt(a2)
grad(b) = deriv(b)_(a1), deriv(b)_(a2) = 1/(2*sqrt(a1)), 1/(2*sqrt(a2)) = 
= 1/(2*10^-2), 1/(2*(1 + O(10^-4))) = 
= 50, 0.5 + O(10^-4)

the second term is correct up to the written precision.