To solve the expression [tex]\((\sqrt{a})^2\)[/tex] for any nonnegative real number [tex]\(a\)[/tex], let's understand the properties of square roots and exponents.
The square root of a nonnegative real number [tex]\(a\)[/tex], denoted as [tex]\(\sqrt{a}\)[/tex], is a value that, when multiplied by itself, gives [tex]\(a\)[/tex]. Mathematically, this can be written as:
[tex]\[
\sqrt{a} \cdot \sqrt{a} = a
\][/tex]
Now, let's consider the given expression [tex]\((\sqrt{a})^2\)[/tex]:
1. The square root of [tex]\(a\)[/tex] is [tex]\(\sqrt{a}\)[/tex].
2. When we square [tex]\(\sqrt{a}\)[/tex], we multiply [tex]\(\sqrt{a}\)[/tex] by itself:
[tex]\[
(\sqrt{a})^2 = \sqrt{a} \cdot \sqrt{a}
\][/tex]
3. From the properties of square roots, we know:
[tex]\[
\sqrt{a} \cdot \sqrt{a} = a
\][/tex]
Therefore,
[tex]\[
(\sqrt{a})^2 = a
\][/tex]
So, the correct option is:
B. [tex]\(a\)[/tex]
