Simplify, using \( i \) notation as needed. \( \sqrt{-80} \) The answer is \( \square \). (Simplify your answer. Type an exact answer, using radicals and \( i \) as needed.)

To simplify \( \sqrt{-80} \), we can first express it as \( \sqrt{80} \cdot \sqrt{-1} \). Recognizing that \( \sqrt{-1} = i \), we can rewrite it as: \[ \sqrt{-80} = \sqrt{80} \cdot i \] Next, we simplify \( \sqrt{80} \). The number 80 can be factored into \( 16 \times 5 \), where 16 is a perfect square: \[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] Now, putting it all together, we have: \[ \sqrt{-80} = 4\sqrt{5} \cdot i \] So, the final answer is: \[ 4\sqrt{5} i \]