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 $i = \sqrt{-1}$.