To find the product of [tex]\(\sqrt{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], we follow these steps:
1. Calculate [tex]\(\sqrt{12}\)[/tex]:
[tex]\(\sqrt{12} \approx 3.4641016151377544\)[/tex]
2. Determine the fraction [tex]\(\frac{5}{6}\)[/tex]:
[tex]\(\frac{5}{6} \approx 0.8333333333333334\)[/tex]
3. Multiply [tex]\(\sqrt{12}\)[/tex] by [tex]\(\frac{5}{6}\)[/tex]:
[tex]\[
3.4641016151377544 \times 0.8333333333333334 \approx 2.8867513459481287
\][/tex]
The result of this calculation is approximately [tex]\(2.8867513459481287\)[/tex].
4. Determine the type of number:
Since the product [tex]\(2.8867513459481287\)[/tex] is not a simple fraction or a repeating decimal, it is considered an irrational number.
Therefore, the product of [tex]\(\sqrt{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] is approximately [tex]\(2.8867513459481287\)[/tex], which is an irrational number. The correct option is:
[tex]\[ \boxed{2.8867\ldots; \text{an irrational number}} \][/tex]
