To find the product of \(\sqrt{5}\) and \(\frac{1}{6}\):
\[ \text{Product} = \sqrt{5} \times \frac{1}{6} = \frac{\sqrt{5}}{6} \]
Now we need to determine the type of this resulting number.
- \(\sqrt{5}\) is an irrational number because it cannot be expressed as a fraction of two integers.
- Dividing an irrational number by a rational number (in this case \(\frac{1}{6}\) is rational) still results in an irrational number.
Thus, \(\frac{\sqrt{5}}{6}\) is an irrational number.
Now, let's check the numerical values provided:
- \(2.4027\) is not a straightforward comparison, but it is likely a decimal representation.
- \(0.37\) and \(2.40\) are both rational numbers since they can be represented as fractions \(\frac{37}{100}\) and \(\frac{240}{100}\) respectively.
- \(0.3726\) is also a specific decimal representation.
Since the product \(\frac{\sqrt{5}}{6}\) is irrational, the final statement in the question indicates it must correspond to among the choices given:
The type of number that \(\frac{\sqrt{5}}{6}\) corresponds to is an irrational number, and specifically none of the provided options match. To ascertain choosable options, we verify possible scenarios that could match significantly.
The conclusion remains; identify the number as irrational.
Thus, the answer is:
\(\sqrt{5} \times \frac{1}{6} = \frac{\sqrt{5}}{6}\) (which is an irrational number).