To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \):
First, calculate \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now multiply \( 2\sqrt{3} \) by \( \frac{5}{6} \):
\[ 2\sqrt{3} \cdot \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]
Next, we approximate \( \sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]
Now calculate \( \frac{5\sqrt{3}}{3} \):
\[ \frac{5 \cdot 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867 \]
Thus, the product of \( \sqrt{12} \) and \( \frac{5}{6} \) is approximately \( 2.8867 \).
Since \( \sqrt{3} \) is an irrational number, any non-zero rational multiple of it (like \( 5\sqrt{3}/3 \)) is also irrational.
Therefore, the answer is:
c. 2.8867; an irrational number