Let's find the correct product expression for [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex].
First, recall the property of square roots that states:
[tex]\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\][/tex]
Using this property, we can combine the square roots:
[tex]\[
\sqrt{3} \cdot \sqrt{12} = \sqrt{3 \cdot 12}
\][/tex]
Next, we need to simplify the expression inside the square root:
[tex]\[
3 \cdot 12 = 36
\][/tex]
So the product [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex] simplifies to:
[tex]\[
\sqrt{36}
\][/tex]
Hence, the correct expression that shows the correct product for [tex]\(\sqrt{3} \cdot \sqrt{12}\)[/tex] is:
[tex]\[
\sqrt{36}
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{\sqrt{36}}\)[/tex].
