Write in terms of \( i \). Simplify your answer as much as possible. \[ \sqrt{-80} \]

To simplify \( \sqrt{-80} \), we can first express it using the imaginary unit \( i \), since \( i = \sqrt{-1} \). Start by breaking down the square root: \[ \sqrt{-80} = \sqrt{80} \cdot \sqrt{-1} = \sqrt{80} \cdot i \] Next, simplify \( \sqrt{80} \): \[ \sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] Now substituting back: \[ \sqrt{-80} = 4\sqrt{5} \cdot i \] Thus, the simplified form of \( \sqrt{-80} \) is: \[ 4\sqrt{5}i \]