Question

How do you simplify `5sqrt(-25) • i`?

Answer 1

`-25`

Explanation:

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

In common with all non-zero numbers, `-25` has two square roots.

The square root represented by the symbols `sqrt(-25)` is the principal square root `i sqrt(25) = 5i`. The other square root is `-sqrt(-25) = -i sqrt(25) = -5i`.

When `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`, but that fails if both `a < 0` and `b < 0` as in this example:

`1 = sqrt(1) = sqrt(-1 * -1) != sqrt(-1)*sqrt(-1) = -1`