To simplify the square root expression [tex]$\sqrt{100 x^{36}}$[/tex], we will break it down into simpler components and then compute each part.
1. Simplify the constant:
Consider the square root of the constant term 100:
[tex]\[
\sqrt{100} = 10
\][/tex]
2. Simplify the variable term:
Next, consider the square root of the variable term [tex]\( x^{36} \)[/tex]:
Using the properties of exponents and square roots, we know that:
[tex]\[
\sqrt{x^{36}} = x^{\frac{36}{2}} = x^{18}
\][/tex]
3. Combine the simplified parts:
Putting these simplified components together:
[tex]\[
\sqrt{100 x^{36}} = 10 x^{18}
\][/tex]
Thus, the simplified form of [tex]$\sqrt{100 x^{36}}$[/tex] is:
[tex]\[
10 x^{18}
\][/tex]
From the given options, the correct answer is:
[tex]\[
10 x^{18}
\][/tex]
