For a second I was expecting this to be an April Fool's post about a "fast" way to calculate the inverse of the square root function, i.e. x*x :-)
A lot of times, the code you are writing does distance comparisons to determine overlap or intersection. But if all you are doing is this, then you can use the square of the distance which is just x^2 + y^2 and you have no need for a square root. Some mathematicians call this "quadrance". Or just do all your work in this metric and reserve the square rooting for when it is absolutely necessary.
OK, one very last time. Here are a few previous submissions of this, some of which have comment:
https://news.ycombinator.com/item?id=213056 : Some comments
https://news.ycombinator.com/item?id=419166 : Some comments
https://news.ycombinator.com/item?id=573912
https://news.ycombinator.com/item?id=1599635
https://news.ycombinator.com/item?id=2332793 : Some comments
https://news.ycombinator.com/item?id=3115168 : Some comments
https://news.ycombinator.com/item?id=3259199
https://news.ycombinator.com/item?id=4526609 : Some comments
https://news.ycombinator.com/item?id=4836589
https://news.ycombinator.com/item?id=6106627
https://news.ycombinator.com/item?id=7277215
https://news.ycombinator.com/item?id=7297582