Let's solve the question step-by-step.
Given the expression:
[tex]\[
(\sqrt{a})^2
\][/tex]
where [tex]\(a\)[/tex] is a nonnegative real number.
First, we need to refresh our understanding of the square root and squaring operations:
1. Square Root: The square root of a number [tex]\(a\)[/tex], denoted as [tex]\(\sqrt{a}\)[/tex], is a value that, when multiplied by itself, gives [tex]\(a\)[/tex]. In mathematical terms, [tex]\(\sqrt{a} \times \sqrt{a} = a\)[/tex].
2. Squaring: Squaring a number means multiplying the number by itself. For instance, if [tex]\(x\)[/tex] is a number, then [tex]\(x^2 = x \times x\)[/tex].
According to the properties of square roots and squaring:
[tex]\[
(\sqrt{a})^2 = \sqrt{a} \times \sqrt{a} = a
\][/tex]
Therefore, by applying the definition directly, we can see that when you take the square root of [tex]\(a\)[/tex] and then square it, you get back [tex]\(a\)[/tex].
So, the correct answer is:
A. [tex]\(a\)[/tex]
Thus, for any nonnegative real number [tex]\(a\)[/tex], [tex]\((\sqrt{a})^2 = a\)[/tex].
