To simplify the expression [tex]\(\sqrt{32} \cdot \sqrt{24}\)[/tex], we can use the property of square roots which states that [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex].
So, we have:
[tex]\[
\sqrt{32} \cdot \sqrt{24} = \sqrt{32 \cdot 24}
\][/tex]
Next, we need to calculate the product inside the square root:
[tex]\[
32 \cdot 24 = 768
\][/tex]
This simplifies our expression to:
[tex]\[
\sqrt{768}
\][/tex]
There is no need to simplify this further because it already appears in one of the given options.
Upon comparing with the options provided, we see that option C matches our result.
Thus, the correct answer is:
C. [tex]\(\sqrt{768}\)[/tex]
