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

Take the square root, it’s not an integer.

Edit, an acre is defined as “43560 square feet” but that can take any shape. It’s not a square.

A perfect square ending in zero must end with an even number of zeroes.

@Zounderkite , That is correct. Another way of saying this is that the number of zeros from the multiplication is twice the number of zeros at the end of the number being squared, which must be even, and includes the case where the last digit is not zero (zero zeros), since two times zero is zero.

Perfect squares are in the form x times x, so they form a continuous curve of increasing values. So when I look at this question (after getting the snarky “I don’t care” type reactions out of my system), my first thought is to just estimate and look and the values around it to see.

So:
200×200 = 40000
210×210 = 44100
209×209 = 43681

At this point, I am certain it’s not a perfect square, because the next closest possible number would be 208, and that’s clearly going to be a lower value, just looking at the values above.

Just for completeness:
208×208 = 43264

P.S. You check things with ChatGPT??? Wow, that seems like the opposite of mathematical rigor.

@Zaku , Look at all the work you had to put in compared to @Zounderkite. That approach is also easy to generalize.

You are correct about my use of ChatGPT, but I have good luck so far in asking it relatively straightforward questions.