Can you easily show why 43,560 is not a perfect square?

I came upon the fact that an acre is 43,560 square feet. My first impulse was to think that an acre must be based on a square patch. To find the size of such a square I would need to take the square root of 43,560. After thinking about it, it was clear that 43,560 cannot be a perfect square. Do you see why?

A check with ChatGPT showed that the original definition of an acre was the area of a rectangle of length one furlong (660 feet) and width of one chain (66 feet) in the old English measuring system.