Question

What is the `sqrt(-25)`?

Answer 1

`sqrt(-25) = 5i`

Explanation:

`-25` has two square roots `5i` and `-5i`, but the expression `sqrt(-25)` denotes the principal square root, which by convention is `5i`.

In general, if `x < 0` then `sqrt(x) = (sqrt(-x))i`. Hence in our example:

`sqrt(-25) = (sqrt(25))i = (sqrt(5^2))i = 5i`