Knowing how to do a square root efficiently by hand is probably a bit overkill, although it can still be useful sometimes. I was rather arguing about addition,

Knowing how to do a square root efficiently by hand is probably a bit overkill, although it can still be useful sometimes. I was rather arguing about addition, division etc., which come up much more often in back-of-the-envelope calculations; and which also provide a much easier and earlier introduction to the kind of algorithmic thinking that is required in algebra, programming etc.