So, what’s the quickest/simplest/correct way to get Perl to act like the calculator app that comes with Windows ...

With the emphasis on "calculator app" Gnu Octave could be an option. There is the Inline::Octave module that lets you Inline octave code into your perl.

I haven't tried it yet so I don't know if it's quick and easy and probably you'll find it to heavyweight for only calculating roots.