The stupid question is the question not asked  
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computing square root by hand  no sqrt (golf, beginner)by boo_radley (Parson) 
on May 09, 2002 at 18:05 UTC ( #165450=perlmeditation: print w/ replies, xml )  Need Help?? 
I ran across this Dr. Math faq and thought it would make a nifty intro to perl golf( in that the algorithm is pretty simple).
your script should take 2 inputs on the command line, the first being the number we're looking for the root of, and a first 'best guess' Again, don't use sqrt in your code. Stop guessing when you have a reasonable idea of what the answer is, and print it out. Your code isn't responsible for error checking or verifying that the output's correct (verify it with a calculator if you like). here's an outline of the algorithm described in the first section of the above url: First, start by guessing a square root value. It helps if your guess is a good one but it will work even if it is a terrible guess. We will guess that 2 is the square root of 12. In step two, we divide 12 by our guess of 2 and we get 6. In step three, we average 6 and 2: (6+2)/2 = 4 Now we repeat step two with the new guess of 4. So 12/4 = 3 Now average 4 and 3: (4+3)/2 = 3.5 Repeat step two: 12/3.5 = 3.43 Average: (3.5 + 3.43)/2 = 3.465 some sample input/output : All of these have have a precision of 3 digits. my answer, at 66 characters, below :
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