Question

Find the product of $\sqrt {5}$ and $\frac {1}{6}$ . What type of number is it? (1 point)
2.4027 __ : an irrational number
0.37: a rational number
2.40; a rational number
0.3726 __ : an irrational number

Answer 1

Select one of the selected answers

Answer 2

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.

1. \(\sqrt{5}\) is an irrational number because it cannot be expressed as a fraction of two integers.
2. 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**).

Answer 3

The product of \(\sqrt{5}\) and \(\frac{1}{6}\) is \(\frac{\sqrt{5}}{6}\), which is an irrational number.

Among the provided choices, the correct selection is:

**2.4027: an irrational number**

This is the only irrational number presented.