To simplify the expression [tex]\(\sqrt{16 x^2}\)[/tex], follow these steps:
1. Rewrite the radical expression:
[tex]\[
\sqrt{16 x^2}
\][/tex]
2. Express the product under the square root:
[tex]\[
\sqrt{16 \cdot x^2}
\][/tex]
3. Break the square root into separate factors:
[tex]\[
\sqrt{16} \cdot \sqrt{x^2}
\][/tex]
4. Simplify each square root:
[tex]\[
\sqrt{16} = 4
\][/tex]
[tex]\[
\sqrt{x^2} = |x|
\][/tex]
Therefore:
[tex]\[
\sqrt{16 x^2} = 4 \cdot |x|
\][/tex]
The simplified form of [tex]\(\sqrt{16 x^2}\)[/tex] is [tex]\(4 |x|\)[/tex].
However, if we are given the options and considering a conventional approach where [tex]\(x\)[/tex] is typically taken to be positive (so [tex]\(\sqrt{x^2} = x\)[/tex]), the simplified form can be written as:
[tex]\[
4 \cdot x = 4x
\][/tex]
The correct answer is:
a) [tex]\(4x\)[/tex].
