To find the simplified form of [tex]\(\sqrt{400 x^{100}}\)[/tex], let's break down the expression step by step.
1. Square Root of the Constant:
[tex]\[
\sqrt{400} = 20
\][/tex]
2. Simplify the Exponent within the Radical:
[tex]\[
\sqrt{x^{100}} = x^{\frac{100}{2}} = x^{50}
\][/tex]
3. Combine the Results:
[tex]\[
\sqrt{400 x^{100}} = 20 \cdot x^{50}
\][/tex]
So, the simplified form of [tex]\(\sqrt{400 x^{100}}\)[/tex] is [tex]\(20 x^{50}\)[/tex].
Therefore, the correct option is:
[tex]\[
\boxed{20 x^{50}}
\][/tex]
