Question

How do you simplify `-9^(1/2)`?

Answer 1

`3i`

Explanation:

Anything raised to the `1/2` is equivalent to the square root of that value.

`-9^(1/2)`

`sqrt(-9)`

Now we have the square root of a negative number. We can change this into an imaginary number. The square root of a negative number is equal to that number `i`. For example:

`sqrt(- x) = x i`

So in this case:

`sqrt(-9) = 3i`

Answer 2

`+-3i`

Explanation:

There is ambiguity in the question. To remove it let

1. `-9^(1/2)` can be written as
   `-1xx9^(1/2)`
   `=>(-1)xx(+-3)`
   `=>+-3`
   As reverse is not true, hence supposition is not correct.
2. `-9^(1/2)` can also be written as
   `(-1)^(1/2)xx9^(1/2)`
   `=>ixx+-3`
   `=+-3i`
   As reverse is always true

Hence `+-3i` is the correct answer.