To simplify the expression [tex]\(\sqrt{36y^3}\)[/tex], follow these steps:
1. Break down the square root of the product into the product of square roots:
[tex]\[
\sqrt{36y^3} = \sqrt{36} \cdot \sqrt{y^3}
\][/tex]
2. Simplify the square root of [tex]\(36\)[/tex]:
[tex]\[
\sqrt{36} = 6
\][/tex]
3. Simplify the square root of [tex]\(y^3\)[/tex]:
[tex]\[
\sqrt{y^3} = y^{3/2}
\][/tex]
Combining these results:
[tex]\[
\sqrt{36y^3} = 6 \cdot y^{3/2}
\][/tex]
Thus, the simplified form of the expression [tex]\(\sqrt{36y^3}\)[/tex] is:
[tex]\[
6y^{1.5} \quad \text{or} \quad 6y^{3/2}
\][/tex]
In this problem's multiple choices, the closest answer provided to our simplified form is:
a) [tex]\(6y\)[/tex], but this doesn't match exactly. It seems there might be an error in the provided choices as none of them match [tex]\(6y^{3/2}\)[/tex].
