use strict;
use warnings;
use POSIX 'ceil';

my $digits = 6;
my $fd = $digits/2;
my ($lo, $hi) = ((9 x ($digits-1))+1, 9 x $digits);
for my $sqrt (ceil(sqrt $lo) .. int(sqrt $hi)) {
  my $prod = $sqrt * $sqrt;
  next if substr($prod, $fd, 1) eq '0';
  my ($f1, $f2) = (substr($prod, 0, $fd), substr($prod, $fd));
  print "$f1 + $f2 = $sqrt, the root of $prod\n" if $f1 + $f2 == $sqrt;
}