To simplify the expression [tex]\(\sqrt{e^2}\)[/tex] for any nonnegative real number [tex]\(e\)[/tex], let's follow these steps:
1. Understand the Components:
- [tex]\(e\)[/tex] is a nonnegative real number, meaning [tex]\(e \geq 0\)[/tex].
- [tex]\(\sqrt{e^2}\)[/tex] represents the square root of [tex]\(e\)[/tex] squared.
2. Apply the Definition of Square Root:
- The square of [tex]\(e\)[/tex] is [tex]\(e^2\)[/tex].
- The square root function, denoted by [tex]\(\sqrt{\cdot}\)[/tex], is the inverse operation of squaring, and it yields the nonnegative value that, when squared, gives back the original number.
3. Simplify the Expression:
- We are looking for the nonnegative value that when squared results in [tex]\(e^2\)[/tex].
- For nonnegative [tex]\(e\)[/tex], the square root of [tex]\(e^2\)[/tex] is simply [tex]\(e\)[/tex].
Thus, [tex]\(\sqrt{e^2} = e\)[/tex].
Therefore, the expression [tex]\(\sqrt{e^2}\)[/tex] simplifies to [tex]\(e\)[/tex] for any nonnegative real number [tex]\(e\)[/tex].
Hence, the correct choice is:
C. [tex]\(e\)[/tex]
