Asking for suggestions about square numbers

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Please let me excuse first. It is embarrassing but I know nothing about math; but when I played with the square numbers with my calculator while slacking of my paper work yesterday (like, press 4 then √, then 9 and √, 16 and √; continuously until I got bored~ haha...), it happened to extend further.. (please see the photos)

Excuse me if it looks confusing and messy, I have no idea what I was writing, too

I just found it interesting and quite fun, and it made my brain fresh. I want to read about it but I do not know how to search for it, I do not know any key words or what is it about, because I threw math back to the teacher's face since I finished high school . Nearly 20 years ago...

I would like to ask what is this kind called, and can I have some links to tables like this to learn it more, please.

(Is this even math... I wonder...)

Thank you in advanced!

P.S. I cannot embed the photos yet, please follow the links.

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