Alright, let's find the simplified product step by step.
Given:
[tex]\[
\sqrt{2x^3} \cdot \sqrt{18x^5}
\][/tex]
1. Combine the expressions under a single square root:
[tex]\[
\sqrt{2x^3} \cdot \sqrt{18x^5} = \sqrt{(2x^3) \cdot (18x^5)}
\][/tex]
2. Multiply the terms inside the square root:
[tex]\[
\sqrt{2 \cdot 18 \cdot x^3 \cdot x^5} = \sqrt{36x^8}
\][/tex]
3. Simplify the square root expression:
[tex]\[
\sqrt{36x^8} = \sqrt{36} \cdot \sqrt{x^8}
\][/tex]
Here, [tex]\(\sqrt{36} = 6\)[/tex] and [tex]\(\sqrt{x^8} = x^4\)[/tex] (since [tex]\( \sqrt{x^8} = (x^8)^{1/2} = x^{8/2} = x^4 \)[/tex]).
4. Combine the simplified parts:
[tex]\[
\sqrt{36} \cdot \sqrt{x^8} = 6x^4
\][/tex]
So, the simplified product is:
[tex]\[
6 x^4
\][/tex]
By comparing with the given options, the correct answer is:
[tex]\[
6 x^4
\][/tex]
