Here is issue with initialisation of array(@values = ();). It is reinitialising on every iteration of loop and ultimately storing last value. Use below hope that will fulfil your requirement

!#/usr/bin/perl

use strict;
use warnings;

@number = qw(1 2 3 4 5 10 11 12 13 14);

print "The values within the array are @number\n\n";

print "We will now print the square root of each number in the array a
+s long as it falls between the range of 100-200 \n\n";
my @values = ();
foreach $num (@number)
{
$sq = $num * $num;
if ($sq >= 100 && $sq <= 200)
{

push(@values, $sq);
}
}
print "Obtaining square values using foreach loop: @values\n";
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