Just extracting the awesome result (with minor simplification):

> To evaluate c = sqrt(a^2+b^2), assuming a is the larger number (if it is not, swap them):

> Compute c = max(a, 0.9a+0.5b)

> Done! That’s the result. This is an estimation and it does come with an error, but the error is at worst 3 %, and on average it is 1.5 %.