Write in terms of \( i \), Simplify your answer as much as pessible, \[ \sqrt{-144} \]

To simplify \(\sqrt{-144}\) in terms of the imaginary unit \(i\), follow these steps: 1. **Express the negative number using \(i\):** Recall that \(i\) is defined as the square root of \(-1\): \[ i = \sqrt{-1} \] 2. **Factor the negative number inside the square root:** \[ \sqrt{-144} = \sqrt{144 \times (-1)} \] 3. **Separate the square root of the product into the product of square roots:** \[ \sqrt{144 \times (-1)} = \sqrt{144} \times \sqrt{-1} \] 4. **Simplify each part:** - \(\sqrt{144} = 12\) - \(\sqrt{-1} = i\) Therefore: \[ \sqrt{144} \times \sqrt{-1} = 12i \] 5. **Final Answer:** \[ \sqrt{-144} = 12i \] So, \(\sqrt{-144}\) simplified in terms of \(i\) is: \[ \boxed{12i} \]