In practice the difference between constant factors is usually between 10 and 10^4, while input size can go up to 10^10 and more, so factors of sqrt(n) or highe

In practice the difference between constant factors is usually between 10 and 10^4, while input size can go up to 10^10 and more, so factors of sqrt(n) or higher will usually always matter, while factors of log(n) or lower will often not matter, and factors in between will depend.