units are not compatible

On second thought ... you don't need to divide by the units at all! Why are you doing so?

The formula you use seems to be unit-aware anyway (not a empirical formula).

It also looks to me that the result shown above is wrong because the variables involved are vectors. So the result of the second summand in the root is calculated as a vector dot product. I guess this is not what you intend!

To avoid this you always should apply vectorization if you are working with vectors but don't want operations like a product don't be seen as vector product but rather apply it singly to each vector element.

You can clearly see that the results are different now!