This saves a great deal of time, as the sqrt() function is relativly expensive.

That used to be the true in the old times, when sqrt was calculated by software and the languages were simple. Well, simple languages still exist, but at least for Perl, the overhead of creating and destroying variables, moving things around and executing the opcodes are more important than what takes your hardware to do the floting point operations. Just see this benchmark for an example:

use Benchmark ':all';

our $a = 347.3;
our $b = 876.1;
our $c;

cmpthese( 5_000_000, 
    {
        'rand' => sub { rand() },
        add => sub { $c = $a + $b },
        mul => sub { $c = $a * $b },
        div => sub { $c = $a / $b },
        'sqrt' => sub { $c = sqrt($b) },
    }
);
[download]

Benchmark: timing 5000000 iterations of add, div, mul, rand, sqrt...
       add:  2 wallclock secs ( 1.32 usr +  0.00 sys =  1.32 CPU) @ 3787878.79/s (n=5000000)
       div:  1 wallclock secs ( 1.58 usr +  0.00 sys =  1.58 CPU) @ 3164556.96/s (n=5000000)
       mul:  2 wallclock secs ( 1.50 usr +  0.00 sys =  1.50 CPU) @ 3333333.33/s (n=5000000)
      rand:  1 wallclock secs ( 1.15 usr +  0.00 sys =  1.15 CPU) @ 4347826.09/s (n=5000000)
      sqrt:  0 wallclock secs ( 1.18 usr +  0.01 sys =  1.19 CPU) @ 4201680.67/s (n=5000000)
          Rate  div  mul  add sqrt rand
div  3164557/s   --  -5% -16% -25% -27%
mul  3333333/s   5%   -- -12% -21% -23%
add  3787879/s  20%  14%   -- -10% -13%
sqrt 4201681/s  33%  26%  11%   --  -3%
rand 4347826/s  37%  30%  15%   3%   --

Surprise! sqrt and rand may even be faster! The results are not entirely reproducible, but the short answer is: it doesn't really matter. As I said in a previous post, the problem here is the type of algorithm and how it scales.