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To solve this, we need to simplify \( 2 \sqrt{-32} \).

### Step-by-Step Solution:
1. **Handle the Negative Inside the Square Root:**
   \[
   \sqrt{-32} = \sqrt{-1 \cdot 32} = \sqrt{-1} \cdot \sqrt{32}
   \]
   Since \(\sqrt{-1} = i\) (where \(i\) is the imaginary unit), we get:
   \[
   \sqrt{-32} = i \cdot \sqrt{32}
   \]

2. **Simplify \(\sqrt{32}\):**
   Break down 32 into factors:
   \[
   \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
   \]
   Thus,
   \[
   \sqrt{-32} = i \cdot 4\sqrt{2} = 4i\sqrt{2}
   \]

3. **Multiply by 2:**
   Now we go back to the original expression, \(2 \cdot \sqrt{-32}\):
   \[
   2 \cdot \sqrt{-32} = 2 \cdot (4i\sqrt{2}) = 8i\sqrt{2}
   \]

### Conclusion:
The correct answer is:
\[
\boxed{8i\sqrt{2}}
\]

Would you like more details, or do you have any questions about the solution?

Here are some related questions to practice:

1. What is \( \sqrt{-64} \) simplified?
2. How would you simplify \( 3 \sqrt{-18} \)?
3. What is the value of \( \sqrt{-50} \) in terms of \( i \)?
4. If \( \sqrt{-72} \) is simplified, what would the result be?
5. What is the simplified form of \( 5 \sqrt{-8} \)?

**Tip:** Remember that \( i \) represents \( \sqrt{-1} \), and this is essential when dealing with square roots of negative numbers.

Learn how to simplify the complex expression 2√−32 using imaginary numbers and radicals. This problem covers key concepts in complex numbers, the imaginary unit i, and simplification techniques. Suitable for high school students.

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