Cage: The square root (or, conversely, the second power) is a strictly increasing function on the non-negative numbers. If a value is above the original threshold, then the square of that value will be above the squared threshold. If a value is below the original threshold, the squared value will be below the squared threshold. The fact that the range of your values increases does not matter, since all you're interested in is their ordering by size which - I'll say it again - doesn't change if you square or take the square root.

-- I'm not mad at you, just Westphalian.