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The question asks, "Which of the following is not an element of **ℝ** (the set of real numbers)?"

Let’s analyze each option:

a) \(-7\):  
   \(-7\) is a real number because it is a negative integer. So, this is in \(\mathbb{R}\).

b) \(-\sqrt{7}\):  
   \(\sqrt{7}\) is a real number, and multiplying it by \(-1\) gives a negative real number. Therefore, \(-\sqrt{7}\) is also in \(\mathbb{R}\).

c) \(\sqrt{-7}\):  
   The square root of a negative number is not a real number; it is an imaginary number. Specifically, \(\sqrt{-7}\) belongs to the set of complex numbers, not the real numbers. Therefore, this is **not** in \(\mathbb{R}\).

d) \(\pi\):  
   \(\pi\) is a real number (an irrational number). Thus, \(\pi\) is in \(\mathbb{R}\).

**Conclusion:** The correct answer is **c) \(\sqrt{-7}\)** because it is not a real number.

Would you like more details or have any questions? Here are five related questions to consider:

1. What are the key differences between real and imaginary numbers?
2. How do we classify irrational numbers like \(\pi\) in the real number system?
3. What is the definition of a complex number?
4. How do operations like square roots affect the classification of a number as real or complex?
5. How do we handle negative numbers under a square root in algebraic contexts?

**Tip:** The square root of a negative number always results in an imaginary number, represented as \(i\), where \(i = \sqrt{-1}\).

Which of the following is not an element of ℝ?

Determine which number is not part of the real number system. This problem covers key mathematical concepts, including real and imaginary numbers, square roots, and complex numbers. Suitable for students in Grades 9-12.

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