What is his algorithm of taking square of a 5 digit number?

Question

I was watching this TED talk: Mathemagics and the performer, as his final trick, attempts to square a 5 digit number in a fairly short amount of time by as well thinking out loud (starting at 11:00, well actually 13:52). What is his algorithm?

Answer 1

Here is the optimal algorithm for multiplication:

https://eprint.iacr.org/2006/224.pdf

Answer 2

I didn't follow perfectly, but I believe he did $57683^2=(57000+683)^2=57^2\cdot 10^6 + 2000\cdot 57\cdot 683 +683^2=57^2\cdot 10^6 + 2000\cdot 57\cdot 683 + (700-17)^2$, which is similar to how normal people multiply but grouping into two digit chunks. He seemed to know $57^2$ without calculation, which I find quite believable. Stage calculators usually have a large number of facts memorized. I have seen the claim that some knew the multiplication table up to $100 \times 100$. I don't know how he did the middle term.