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 : 
C:\>sqrt 701 25
26.4764404223228

C:\>sqrt 12 2
3.46428571428571

C:\>sqrt 120 10
10.9544511505092

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All of these have have a precision of 3 digits.

my answer, at 66 characters, below : 
($n,$_)=@ARGV;while(1){$_=($_+$n/$_)/2;($l^$_)||print&&exit;$l=$_}

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Replies are listed 'Best First'.
Re: computing square root by hand -- no sqrt (golf, beginner)
by japhy (Canon) on May 09, 2002 at 18:17 UTC
    Golfing to 59: 
    ($n,$_)=@ARGV;{$l^($_=($_+$n/$_)/2)||exit print;$l=$_;redo}

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    _____________________________________________________
    Jeff[japhy]Pinyan: Perl, regex, and perl hacker, who'd like a job (NYC-area)
    s++=END;++y(;-P)}y js++=;shajsj<++y(p-q)}?print:??;

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      a reinterpretation of japhy's solution gives 54:
      $_=pop;$l^$_?$l=$_:die"$_\n"while$_=($_+$ARGV[0]/$_)/2

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      jynx

      update: this works at 53:

      $_=pop;$l^$_?$l=$_:die"$_\n"while($_+=$ARGV[0]/$_)/=2

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      update2: using the comma instead of quotes for die it's 52:
      $_=pop;$l^$_?$l=$_:die$_,$/while($_+=$ARGV[0]/$_)/=2

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Re: computing square root by hand -- no sqrt (golf, beginner)
by Matts (Deacon) on May 09, 2002 at 19:49 UTC
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      print $ARGV[0]**.5

      This is the best answer I've seen in this thread :) It's clear, short and very precise...
      How about some golfing while you're at it? 

      die+shift()**.5,$/

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      I know that this is 18 strokes like yours, but this one prints a newline ;) 

      - Yes, I reinvent wheels.
- Spam: Visit eurotraQ.

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        Since you're only using one argument you can call it with one argument and shorten it to 16:
        die pop()**.5,$/

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        but that's bending the rules...
        jynx
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      How's 17? The space is unnecessary. 
         MeowChow                                   
               s aamecha.s a..a\u$&owag.print
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Re: computing square root by hand -- no sqrt (golf, beginner)
by jynx (Priest) on May 09, 2002 at 21:01 UTC

    While playing around, i thought i would (jokingly) try to golf Matt's solution and found something interesting. Using subtraction instead of bit-xor is more accurate. So, cleaning up my current mess of solutions and using subtraction for accuracy, it's now 49 chars (52 to print a carriage return):
    #23456789_123456789_123456789_123456789_123456789_123456789_
$_=pop;$l=$_,($_+=$ARGV[0]/$_)/=2while$l-$_;print

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    jynx

    update:an approximation method:

    # 44
#23456789_123456789_123456789_123456789_123456789_
$a=pop;($a+=$ARGV[0]/$a)/=2for-9..99;print$a

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Re: computing square root by hand -- no sqrt (golf, beginner)
by particle (Vicar) on May 09, 2002 at 19:51 UTC
    mine at 57:

    #0        1         2         3         4         5         6
#123456789012345678901234567890123456789012345678901234567890
 $_=pop,$n=pop;{$l^($_=($_+$n/$_)/2)||die$_,$/;$l=$_;redo}

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    ~Particle *accelerates*

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(MeowChow) Re: computing square root by hand -- no sqrt (golf, beginner)
by MeowChow (Vicar) on May 10, 2002 at 10:16 UTC
    38 chars, note that the second argument is entirely superfluous:
      
    ($_+=$ARGV[0]/$_)/=2for($_=1)x99;print

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       MeowChow                                   
               s aamecha.s a..a\u$&owag.print
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Re: computing square root by hand -- no sqrt (golf, beginner)
by cLive ;-) (Prior) on May 10, 2002 at 09:45 UTC
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Re: computing square root by hand -- no sqrt (golf, beginner)
by pepik_knize (Scribe) on May 13, 2002 at 18:22 UTC
    44 using both arguments, but no \n. Add 3 for -l to get it.
    0        1         2         3         4
12345678901234567890123456789012345678901234
$b=pop;$b=($b+$ARGV[0]/$b)/2for 0..9;print$b

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    Pepik
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