Question

Find the product of square root 5 and 1/6. What type of number is it?

0.37; A rational number
2.40; A rational number
0.3726...; An irrational number
2.4027...; An irrational number

Answer 1

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:

\[
0.3726...; \text{ An irrational number}
\]