To find the product of \(\sqrt{5}\) and \(\frac{1}{6}\), we can calculate:
\[ \sqrt{5} \times \frac{1}{6} = \frac{\sqrt{5}}{6} \]
Next, we need to determine if \(\frac{\sqrt{5}}{6}\) is a rational or irrational number.
- A rational number can be expressed as a fraction of two integers (\(a/b\)), where \(b \neq 0\).
- An irrational number cannot be expressed as a fraction of two integers.
Since \(\sqrt{5}\) is irrational, \(\frac{\sqrt{5}}{6}\) is also irrational (the product of a non-zero rational number and an irrational number is irrational).
Now we can compute the approximate value of \(\sqrt{5}\):
\[ \sqrt{5} \approx 2.236 \]
Thus, we calculate:
\[ \frac{\sqrt{5}}{6} \approx \frac{2.236}{6} \approx 0.372666... \]
This value matches with the provided option \(0.3726...\), which is an approximation of this irrational number.
So, the final answer is:
\[ 0.3726...; \text{ An irrational number} \]
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