Sure, let's solve the expression [tex]\(\sqrt{36 x^8}\)[/tex] step-by-step.
1. Write down the given expression:
[tex]\[
\sqrt{36 x^8}
\][/tex]
2. Simplify the square root of the constant term:
The constant term inside the square root is 36. The square root of 36 is:
[tex]\[
\sqrt{36} = 6
\][/tex]
3. Simplify the square root of the variable term:
The variable term inside the square root is [tex]\(x^8\)[/tex].
To simplify [tex]\(\sqrt{x^8}\)[/tex], we recognize that:
[tex]\[
\sqrt{x^8} = x^{\frac{8}{2}} = x^4
\][/tex]
4. Combine the simplified parts:
Putting together the simplified square root of the constant and variable terms, we get:
[tex]\[
6 \cdot \sqrt{x^8} = 6 \cdot x^4
\][/tex]
However, [tex]\(\sqrt{x^8}\)[/tex] can also be expressed as [tex]\( (x^4)^2 \)[/tex], which further simplifies to [tex]\(x^4\)[/tex] only when taken outside the square root.
Thus, the simplified expression remains:
[tex]\[
6 \sqrt{x^8}
\][/tex]
Thus, the final simplified form of the expression is:
[tex]\[
6 \sqrt{x^8}
\][/tex]
