This note in three or four parts by John Conway is full of delicious Aha insights. The first item about the square of root was discovered in the 50’s of last century by Tennenbaum, as mentioned in the very enjoyable paper elaborating on this item, by Steven Miller and David Montague, Irrationality from the book (Arxive 2018).
The power of Mathematics https://janwillemklop.com/wp-content/uploads/2024/02/powerofmathematics.pdf
