Evaluate the​ expression, or state that the expression is not a real number.
StartRoot negative 4 EndRoot
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The expression is a real number. StartRoot negative 4 EndRootequals
  
enter your response here ​(Simplify your​ answer.)
B.
The expression is not a real number.

To evaluate \( \sqrt{-4} \), let's recall that taking the square root of a negative number does not result in a real number. In the realm of real numbers, square roots of negative numbers are undefined because there is no real number that, when squared, yields a negative result.

Thus, the expression \( \sqrt{-4} \) is **not a real number**.

The correct answer is:
**B. The expression is not a real number.**

Would you like further details, or do you have any questions?

Here are 5 related questions for further exploration:
1. How would you evaluate \( \sqrt{-9} \) in terms of imaginary numbers?
2. What is the principal square root of \( 4 \) in the real number system?
3. How does the concept of imaginary numbers extend the set of real numbers?
4. Can the square root of a negative number ever be simplified to a real number?
5. What are the rules for adding and subtracting square roots of negative numbers?

**Tip:** Remember that for square roots of negative numbers, we can use the imaginary unit \( i \) where \( i = \sqrt{-1} \). For example, \( \sqrt{-4} = 2i \) in the complex number system.

Evaluate the expression, or state that the expression is not a real number. StartRoot negative 4 EndRoot.

Understand why the square root of negative numbers, such as √-4, is not a real number and how imaginary numbers provide a solution. Learn the rules for working with square roots of negative numbers, suitable for Grades 9-11.

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