Write in terms of \( i \). Simplify your answer as much as possible. \( \sqrt{-44} \)

To express \( \sqrt{-44} \) in terms of \( i \), we first recognize that \( \sqrt{-44} = \sqrt{44} \cdot \sqrt{-1} \). Since \( \sqrt{-1} = i \), we can rewrite this as: \[ \sqrt{-44} = \sqrt{44} \cdot i \] Now, we simplify \( \sqrt{44} \). We can factor 44 into \( 4 \times 11 \), so: \[ \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \cdot \sqrt{11} = 2\sqrt{11} \] Putting it all together, we have: \[ \sqrt{-44} = 2\sqrt{11} \cdot i \] Therefore, the simplified expression for \( \sqrt{-44} \) is: \[ 2\sqrt{11}i \]