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

Jun 30, 2016

$3 i$

#### Explanation:

Anything raised to the $\frac{1}{2}$ is equivalent to the square root of that value.

$- {9}^{\frac{1}{2}}$

$\sqrt{- 9}$

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:

$\sqrt{- 9} = 3 i$

Jun 30, 2016

$\pm 3 i$

#### Explanation:

There is ambiguity in the question. To remove it let

1. $- {9}^{\frac{1}{2}}$ can be written as
$- 1 \times {9}^{\frac{1}{2}}$
$\implies \left(- 1\right) \times \left(\pm 3\right)$
$\implies \pm 3$
As reverse is not true, hence supposition is not correct.
2. $- {9}^{\frac{1}{2}}$ can also be written as
${\left(- 1\right)}^{\frac{1}{2}} \times {9}^{\frac{1}{2}}$
$\implies i \times \pm 3$
$= \pm 3 i$
As reverse is always true

Hence $\pm 3 i$ is the correct answer.