Question

What is the square root of -3?

Answer 1

`-3` has no Real square root.

The principal Complex square root of `-3`, denoted `sqrt(-3)` is equal to `i sqrt(3)`, where `i` is the imaginary unit and `sqrt(3)` is the positive square root of `3`.

Explanation:

There is no Real number that is the square root of `-3` since `x^2 >= 0` for all `x in RR`.

`-3` has two Complex square roots, `i sqrt(3)` and `-i sqrt(3)`, where `i` is the imaginary unit, approximately called 'the' square root of `-1`. `i` satisfies `i^2 = -1`.

`sqrt(3)` is the positive square root of `3`.

`-sqrt(3)` is also a square root of `3`, in that `(-sqrt(3))^2 = 3`

`sqrt(-3) = i sqrt(3)` is called the principal square root of `-3`.