To simplify the expression [tex]\(\sqrt{36 x^4}\)[/tex], we can proceed with the following steps:
1. Break down the term inside the square root:
[tex]\[\sqrt{36 x^4}\][/tex]
2. Separate the constants and the variable terms:
[tex]\[\sqrt{36} \cdot \sqrt{x^4}\][/tex]
3. Simplify each part individually:
- The square root of [tex]\(36\)[/tex] is [tex]\(6\)[/tex], because [tex]\(6^2 = 36\)[/tex].
- The square root of [tex]\(x^4\)[/tex] is [tex]\(x^2\)[/tex], because [tex]\((x^2)^2 = x^4\)[/tex].
4. Combine the simplified parts:
[tex]\[6 \cdot x^2\][/tex]
Therefore, the expression [tex]\(\sqrt{36 x^4}\)[/tex] in its simplest form is:
[tex]\[6 x^2\][/tex]
Hence, the correct answer is:
A. [tex]\(6 x^2\)[/tex]
