To simplify the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex], we can follow these steps:
1. Separate the constants and the radicals:
[tex]\[
(6 \sqrt{2})(-3 \sqrt{5}) = (6 \cdot -3) \cdot (\sqrt{2} \cdot \sqrt{5})
\][/tex]
2. Multiply the constants:
[tex]\[
6 \cdot -3 = -18
\][/tex]
3. Multiply the radicals:
[tex]\[
\sqrt{2} \cdot \sqrt{5} = \sqrt{2 \cdot 5} = \sqrt{10}
\][/tex]
4. Combine the results:
[tex]\[
-18 \cdot \sqrt{10}
\][/tex]
Therefore, the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex] simplifies to [tex]\(-18 \sqrt{10}\)[/tex].
The correct answer is:
B. [tex]\(-18 \sqrt{10}\)[/tex]
