Which of the following does [tex]\left(\sqrt{e^2}\right)[/tex] simplify to, for any nonnegative real number [tex]e[/tex]?

A. 1
B. [tex]\sqrt{e}[/tex]
C. [tex]e[/tex]
D. [tex]e^2[/tex]



Answer :

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]