I didn't count them either, I let my computer do that. Actually, it turned out to be more accurate than I thought. When I recalculated it taking the square root of Pi to 2000 places and calculating the answer to 1000 places it was exactly the same.
That's because your computer probably rounded them both to about 4 or 5 places when you "checked" it. I don't think they take it any further.