To find the product of \(\sqrt{12}\) and \(\frac{5}{6}\), we first simplify \(\sqrt{12}\):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we can calculate the product:
\[ 2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3} \]
The product \(\frac{5}{3} \sqrt{3}\) is an irrational number because it is the product of a rational number \(\frac{5}{3}\) and an irrational number \(\sqrt{3}\).
Thus, the final result is:
\[\frac{5}{3} \sqrt{3}\]
And it is an irrational number.