To find the equivalent expression for the product [tex]\(\sqrt{6} \cdot \sqrt{3}\)[/tex], let's work through it step by step.
1. First, we know that the product of two square roots can be combined under a single square root:
[tex]\[
\sqrt{6} \cdot \sqrt{3} = \sqrt{6 \cdot 3}
\][/tex]
2. Next, calculate the product inside the square root:
[tex]\[
6 \cdot 3 = 18
\][/tex]
So the expression is now:
[tex]\[
\sqrt{6} \cdot \sqrt{3} = \sqrt{18}
\][/tex]
3. Now, simplify the square root of 18. We do this by factoring 18 into its prime factors:
[tex]\[
18 = 9 \cdot 2
\][/tex]
4. We know that [tex]\(\sqrt{9 \cdot 2}\)[/tex] can be split into the product of two square roots:
[tex]\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2}
\][/tex]
5. Simplify [tex]\(\sqrt{9}\)[/tex], since [tex]\(9\)[/tex] is a perfect square:
[tex]\[
\sqrt{9} = 3
\][/tex]
6. Therefore, we have:
[tex]\[
\sqrt{18} = 3 \cdot \sqrt{2}
\][/tex]
Thus, the expression [tex]\(\sqrt{6} \cdot \sqrt{3}\)[/tex] simplifies to:
[tex]\[
3 \sqrt{2}
\][/tex]
Therefore, the correct choice is:
B. [tex]\(3 \sqrt{2}\)[/tex]
