To solve the problem of finding the product of [tex]\(\sqrt{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], we can break it down into a few straightforward steps:
1. Compute [tex]\(\sqrt{12}\)[/tex]:
[tex]\[
\sqrt{12} \approx 3.4641016151377544
\][/tex]
This value is already approximated for us.
2. Express the fraction [tex]\(\frac{5}{6}\)[/tex]:
[tex]\[
\frac{5}{6} \approx 0.8333333333333334
\][/tex]
This value is also given in a decimal form.
3. Find the product of these two numbers:
[tex]\[
\sqrt{12} \times \frac{5}{6} \approx 3.4641016151377544 \times 0.8333333333333334
\][/tex]
Performing this multiplication, we get:
[tex]\[
3.4641016151377544 \times 0.8333333333333334 \approx 2.8867513459481287
\][/tex]
Hence, the product of [tex]\(\sqrt{12}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] is approximately [tex]\(2.8867513459481287\)[/tex].
#### Determine the Type of Number:
To determine the type of number, consider that:
- [tex]\(\sqrt{12}\)[/tex] is an irrational number because it cannot be expressed as a simple fraction.
- [tex]\(\frac{5}{6}\)[/tex] is a rational number because it is expressed as a fraction of integers.
When you multiply an irrational number by a rational number (non-zero and non-repeating), the result is typically an irrational number.
Given the numerical result, we can observe:
- [tex]\(2.8867 \ldots \)[/tex] appears to be a non-repeating, non-terminating decimal, which confirms it is an irrational number.
Thus, the correct answer to the question is:
[tex]\[ 2.8867 \ldots \text{ an irrational number} \][/tex]
