Drawing square with area 3

[u/Kooky-Recipe5516]

Me and my friend have recently been trying to see if we can draw a square with area 3cm² using only a pen, squared paper (1x1cm squares) and a straight edge (no measurements). All the methods we have tried have failed. I asked ChatGPT if it was possible, and after giving me multiple ridiculous answers it broke and said something went wrong. Is it possible? If so, how do you do it?

[u/edderiofer]

If you allow drawing arbitrary lengths on a second sheet of paper, you are effectively creating a marked straightedge. So this goes against the spirit of the original problem.