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The question asks to "Choose the correct answer below," with options discussing the square root of a number \( a \).

Let's go through each option:

- **Option A: \( \sqrt{-a} \) is a negative number**
  - This is incorrect. The square root of a number is never negative. However, the expression \( \sqrt{-a} \) is invalid if \( a \) is a positive real number because we cannot take the square root of a negative number within the realm of real numbers.

- **Option B: \( \sqrt{a} \) is the negative square root of \( a \)**
  - This is incorrect. \( \sqrt{a} \) always refers to the principal (positive) square root of \( a \).

- **Option C: \( -\sqrt{a} \) is the positive square root of \( a \)**
  - This is incorrect. \( -\sqrt{a} \) represents the negative square root of \( a \).

- **Option D: \( \sqrt{-a} \) is not a real number**
  - This is the correct answer. The square root of a negative number, such as \( \sqrt{-a} \) where \( a > 0 \), does not exist in the real number system, and is instead represented by an imaginary number.

Thus, the correct answer is **D**: \( \sqrt{-a} \) is not a real number.

Would you like further details or clarification on any part of this? 

Here are 5 related questions:
1. What is the definition of the principal square root?
2. How do we handle square roots of negative numbers in complex numbers?
3. Why is the square root of a negative number not a real number?
4. What does it mean for a number to be imaginary?
5. How can we represent the square root of a negative number using \( i \), the imaginary unit?

**Tip:** The square root symbol \( \sqrt{} \) always refers to the positive (principal) root unless explicitly stated otherwise, like with \( -\sqrt{} \).

Choose the correct answer below: √−a is a negative number, √a is the negative square root of a, −√a is the positive square root of a, or √−a is not a real number.

Explore the properties of square roots and learn why √-a is not a real number. This problem introduces key concepts like the principal square root and the imaginary number i. Perfect for students in grades 9-12.

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