Write in terms of $$ i $$. Simplify your answer as much as possible $$ \sqrt{-7} $$

Question

UpStudy AI · Accepted Answer

To simplify $$\sqrt{-7}$$ in terms of the imaginary unit $$i$$, follow these steps:

1. **Express the negative inside the square root using $$i$$:**
   $$
   \sqrt{-7} = \sqrt{-1 \times 7}
   $$

2. **Separate the square root of the product into the product of square roots:**
   $$
   \sqrt{-1 \times 7} = \sqrt{-1} \times \sqrt{7}
   $$

3. **Recall that $$\sqrt{-1} = i$$:**
   $$
   \sqrt{-1} \times \sqrt{7} = i \times \sqrt{7}
   $$

4. **Combine the terms:**
   $$
   \sqrt{-7} = i\sqrt{7}
   $$

**Final Answer:**
$$
\sqrt{-7} = i\,\sqrt{7}
$$
$$ \sqrt{-7} = i\sqrt{7} $$

Write in terms of \( i \). Simplify your answer as much as possible \[ \sqrt{-7} \]