Challenge 768 Response

Naughty Roots

with Crystalwizard

“Square That Root” appears in issue 768.

Crystalwizard quotes Mathwords to the effect that the square root of a positive — i.e. non-negative — number is considered positive. Even though the product of −3² is +9, we say that the square root of 9 is 3 and let it go at that.

[Don W.] Thanks, Kelly! I really must look up Mathwords some day. Where was it when I was in school and really needed it?

As far as I can make out, negative square roots of positive (“non-negative”) numbers are logical but considered... impolite.

The distinction does seem to be a matter of etiquette. By analogy: in some societies, putting one’s elbows on the dinner table is a no-no (sorry for the double negative!); in others, it’s taken for granted.

To be fair, negative square roots may be logical, but I can’t imagine how they would be of any use. Maybe that’s what Mathwords is trying to tell us.