Question

How do you simplify `sqrt(-9)`?

Answer 1

`sqrt(-9) = 3i`

Explanation:

If `x < 0` then `sqrt(x) = sqrt(-x)i`, where `i` is the imaginary unit.

`i` has the property that `i^2 = -1`

In our example, we find:

`sqrt(-9) = sqrt(9)i = 3i`

Note that special care is required when dealing with square roots of negative numbers. In particular `sqrt(ab) != sqrt(a)sqrt(b)` if both `a < 0` and `b < 0`.

For example:

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