To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we first calculate \( \sqrt{12} \).
The square root of 12 can be simplified as follows:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we can multiply this by \( \frac{5}{6} \):
\[ \frac{5}{6} \times \sqrt{12} = \frac{5}{6} \times 2\sqrt{3} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]
Next, we need to evaluate \( \sqrt{3} \) to find an approximate value of \( \frac{5\sqrt{3}}{3} \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \).
Calculating:
\[ \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867 \]
Thus, the product \( \frac{5\sqrt{3}}{3} \) is approximately \( 2.8867 \).
Since \( \sqrt{3} \) is an irrational number, \( \frac{5\sqrt{3}}{3} \) is also an irrational number.
Therefore, the answer is:
2.8867 . . . ; an irrational number.
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