To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we first need to calculate it.
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Calculate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
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Now calculate the product: \[ \text{Product} = 2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5 \times \sqrt{3}}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]
Next, we need to find the approximate value of \( \frac{5\sqrt{3}}{3} \):
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Calculate \( \sqrt{3} \) (approximately): \[ \sqrt{3} \approx 1.732 \]
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Now plug this in: \[ \frac{5\sqrt{3}}{3} \approx \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867 \]
This result is approximately \( 2.8867 \).
Finally, since \( \sqrt{3} \) is an irrational number, \( \frac{5\sqrt{3}}{3} \) is also an irrational number.
Thus, the answer is: 2.8867 . . . ; an irrational number