Use the imaginary number $$ i $$ to rewrite the expression below as a complex number. Simplify all radicals. $$ 8+\sqrt{-96} $$ \begin{tabular}{|l}\hline$$ i $$\end{tabular}

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To rewrite the expression $$ 8 + \sqrt{-96} $$ as a complex number, follow these steps:

1. **Express the square root of a negative number using $$ i $$:**
   $$
   \sqrt{-96} = \sqrt{96} \cdot i
   $$

2. **Simplify $$ \sqrt{96} $$:**
   $$
   96 = 16 \times 6 \quad \Rightarrow \quad \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \cdot \sqrt{6} = 4\sqrt{6}
   $$
   
3. **Combine the results:**
   $$
   \sqrt{-96} = 4\sqrt{6} \cdot i
   $$
   
4. **Write the original expression as a complex number:**
   $$
   8 + \sqrt{-96} = 8 + 4\sqrt{6}\,i
   $$

**Final Answer:**
$$
8 + 4\sqrt{6}\,i
$$
$$ 8 + 4\sqrt{6}\,i $$

Use the imaginary number to rewrite the expression below as a complex number. Simplify
all radicals.

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Use the imaginary number to rewrite the expression below as a complex number. Simplify all radicals.