The stupid question is the question not asked  
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Re: [Study]: Searching for square rootsby jimbojones (Friar) 
on Nov 14, 2006 at 14:07 UTC ( #583966=note: print w/ replies, xml )  Need Help?? 
Hi, I think your problem is in your assumption of the maximum possible value for the square root of numbers in the range of 0 to 1. I managed to fix your code with one line to handle the 0.5 case, but I'll leave it to you to find it.
a number between 0 and 1 can be written as 1/x, where x > 1. Then the sqrt(1/x) is sqrt(1)/sqrt(x) = 1/sqrt(x). Now sqrt(x) is < x, so the max value of sqrt(1/x) is 1/x.
 j
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