To solve the problem, let's analyze the expression [tex]\((\sqrt{a})^2\)[/tex] for any nonnegative real number [tex]\(a\)[/tex].
1. Understanding the Square Root:
- The square root function, [tex]\(\sqrt{a}\)[/tex], returns a value [tex]\(b\)[/tex] such that [tex]\(b^2 = a\)[/tex].
- For example, if [tex]\(a = 4\)[/tex], then [tex]\(\sqrt{4} = 2\)[/tex] because [tex]\(2^2 = 4\)[/tex].
2. Squaring the Square Root:
- When we take the square root of [tex]\(a\)[/tex], we get a value [tex]\(\sqrt{a}\)[/tex].
- Squaring [tex]\(\sqrt{a}\)[/tex] would mean raising it to the power of 2: [tex]\((\sqrt{a})^2\)[/tex].
3. Simplification:
- Squaring the square root of a number undoes the square root operation.
- Thus, [tex]\((\sqrt{a})^2\)[/tex] simplifies back to [tex]\(a\)[/tex].
4. Final Result:
- For any nonnegative real number [tex]\(a\)[/tex], the expression [tex]\((\sqrt{a})^2 = a\)[/tex].
Given the choices:
A. [tex]\(\sqrt{a}\)[/tex]
B. [tex]\(a^2\)[/tex]
C. [tex]\(a\)[/tex]
D. 1
The correct choice is C. [tex]\(a\)[/tex].
