Write in terms of $$ i $$. Simplify your answer as much as possible. $$ -\sqrt{-48} $$

Question

UpStudy AI · Accepted Answer

To simplify $$-\sqrt{-48}$$ in terms of $$i$$ (where $$i = \sqrt{-1}$$), follow these steps:

1. **Express the square root of a negative number using $$i$$:**
   $$
   \sqrt{-48} = \sqrt{48} \cdot \sqrt{-1} = \sqrt{48} \cdot i
   $$

2. **Simplify $$\sqrt{48}$$:**
   $$
   \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
   $$

3. **Combine the results:**
   $$
   \sqrt{-48} = 4\sqrt{3} \cdot i
   $$

4. **Include the negative sign:**
   $$
   -\sqrt{-48} = -4\sqrt{3} \cdot i
   $$

**Final Simplified Form:**
$$
-4\sqrt{3}\,i
$$
$$-4\sqrt{3}\,i$$

Write in terms of \( i \). Simplify your answer as much as possible. \[ -\sqrt{-48} \]