use Math::Big::Factors; my $val = 2000; my @x = Math::Big::Factors::factors_wheel( $val ); print "@x\n"; my %factors; $factors{$_}++ for @x; use Data::Dumper; print Dumper \%factors; my $sqrt = 1; while (my ($k,$v) = each %factors) { while ($v > 1) { $sqrt *= $k; $v -= 2; } if ($v) { $sqrt *= sqrt( $k ); } } print "$sqrt => ", sqrt( $val ), $/;