To simplify the expression [tex]\(\sqrt{36 x^6 y^4}\)[/tex], we can follow these steps:
1. Simplify the constant inside the square root:
[tex]\[
\sqrt{36} = 6
\][/tex]
2. Simplify the variable terms inside the square root:
- For [tex]\(x^6\)[/tex]:
[tex]\[
\sqrt{x^6} = x^3
\][/tex]
This is because [tex]\(\sqrt{(x^3)^2} = x^3\)[/tex].
- For [tex]\(y^4\)[/tex]:
[tex]\[
\sqrt{y^4} = y^2
\][/tex]
This is because [tex]\(\sqrt{(y^2)^2} = y^2\)[/tex].
3. Combine all simplified parts:
[tex]\[
\sqrt{36 x^6 y^4} = \sqrt{36} \cdot \sqrt{x^6} \cdot \sqrt{y^4} = 6 \cdot x^3 \cdot y^2
\][/tex]
Therefore, the simplified form of the expression [tex]\(\sqrt{36 x^6 y^4}\)[/tex] is:
[tex]\[
6x^3y^2
\][/tex]
