Sure! Let's go step-by-step to simplify [tex]\(\sqrt{10} \cdot \sqrt{8}\)[/tex].
1. Multiply the numbers inside the square roots:
[tex]\[
\sqrt{10} \cdot \sqrt{8} = \sqrt{10 \cdot 8}
\][/tex]
Multiply 10 and 8:
[tex]\[
10 \cdot 8 = 80
\][/tex]
So, [tex]\(\sqrt{10} \cdot \sqrt{8}\)[/tex] simplifies to:
[tex]\[
\sqrt{80}
\][/tex]
2. Simplify [tex]\(\sqrt{80}\)[/tex]:
[tex]\[
\sqrt{80} = 8.94427 \quad \text{(rounded to five decimal places)}
\][/tex]
So, the correct answer from the given multiple-choice options is:
[tex]\[
\sqrt{80}
\][/tex]
