To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we first calculate \( \sqrt{12} \).
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now, we multiply this by \( \frac{5}{6} \):
\[ \sqrt{12} \times \frac{5}{6} = 2\sqrt{3} \times \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]
Next, we approximate \( \sqrt{3} \) to calculate the value:
\[ \sqrt{3} \approx 1.732 \]
Now we find \( \frac{5\sqrt{3}}{3} \):
\[ \frac{5\sqrt{3}}{3} \approx \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867 \]
Thus, the product \( \frac{5\sqrt{3}}{3} \) is approximately \( 2.8867 \).
The type of number is an irrational number because \( \sqrt{3} \) is irrational, and the product of an irrational number with a non-zero rational number remains irrational.
The correct response is:
2.8867 . . . ; an irrational number
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