Name: Frank

Question:

In a recent quiz we where asked the square root of four. The quizmaster gave the answer as not only 2 but also -2. Being pedantic I queried this. Although -2 squared is 4, does it follow that the root of 4 is -2 Can you enlighten us?

Regards Frank

Hi Frank,
It depends whether you define "square root of 4" as "the positive number
whose square is 4" or "any number whose square is 4". I think that in
the question "Find **the** square root of 4", the first definition is
implicit, otherwise you should have been asked "Find **all** square roots
of 4".

If the instructions were

then the answer is 2. The surd symbol, applied to a non-negative real number x, always returns the non-negative real number y that satisfies y^{ 2} = x.
Claude and Penny