Question

How to find two square roots of a number?

Answer 1

I will assume that behind this question is a myth that there is such a thing as, for example, "The square root of 2".

In fact for any number `a` (in `RR` or `CC`), if `r` is a square root of `a` then `-r` is also a square root of `a`.

If `a in RR` and `a > 0` then `a` has two real square roots - the positive square root that we represent by the symbols `sqrt(a)` and the negative square root, which is `-sqrt(a)`.

If `a in RR` and `a = 0` then `a` has one (repeated) square root, viz `0`.

If `a in RR` and `a < 0` then `a` has two pure imaginary square roots, `sqrt(-a)*i` and `-sqrt(-a)*i`