I recently need to show this for one problem, and I saw this video on youtube where the creator claims that a number is perfect square if the sum of digits or the digit root (sum of sum of digits and so on..) is 1, 4, 7 or 9.
Here is link to the video: https://www.youtube.com/watch?v=hNj2Fr72as8
I'm not sure how to prove this, can you show me how to start writing the proof.