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

Apr 27, 2016

${\left(- 9\right)}^{\frac{1}{2}} = 3 i$.
${x}^{\frac{1}{2}}$ means $\sqrt{x}$, hence ${\left(- 9\right)}^{\frac{1}{2}}$ is $\sqrt{- 9}$ and it's solution is not possible in real number domain.
However, if the domain is complex numbers, $\sqrt{- 9} = \sqrt{- 1} \times \sqrt{9} = i \times 3 = 3 i$.
Hence ${\left(- 9\right)}^{\frac{1}{2}} = 3 i$.