To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we start by calculating \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Next, we multiply this by \( \frac{5}{6} \):
\[ \sqrt{12} \times \frac{5}{6} = 2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \times \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3} \]
Next, we can approximate \( \sqrt{3} \). The approximate value of \( \sqrt{3} \) is about \( 1.732\). Therefore:
\[ \frac{5}{3} \times 1.732 \approx \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867 \]
Thus, the product \( \sqrt{12} \times \frac{5}{6} \) is approximately \( 2.8867 \).
Now we determine the type of number. Since \( \sqrt{3} \) is an irrational number, and multiplying an irrational number by a rational number (like \( \frac{5}{3} \)) results in an irrational number, \( \frac{5}{3} \sqrt{3} \) is also irrational.
Therefore, the result is:
2.8867 . . . ; an irrational number
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