Well, maybe not square roots, but when I am cutting down a piece of
lumber into thirds or quarters, and it's an unknown length, I measure it
with a steel tape and then do "long division" to get and mark the lengths.
There are still reasons to be able to do simply math in your hand or by
hand.
When you are doing tricks like that it is easier to use the metric
scale on the tape too. No fractions of an inch to fool with
I deal in a lot of equipment installs that are metric and require
drawings in both metric and imperial. Metric is SO much easier and
neater.