This is a great tip that not enough developers know about. In a more general sense: Square roots (or divisions, or other expensive computations) can often be avoided if you’re only interested in if something exceeds a certain threshold (and thus the ‘end result’ such as in this case the actual distance is not needed).

What about relying on a database to handle this for you and use a geospatial query?

PostgreSQL has a fantastic geospatial engine, could easily do it via its queries.

Technically having the threshold as squared and comparing it, is still pythagoreas

Pro tip: Square the distance threshold and compare it with the squared magnitude instead of Pythagoras. Eliminates the incredibly expensive square root.