Question

Find the product of √5
and 1/6
. What type of number is it?(1 point)
Responses

0.37; a rational number
0.37; a rational number

2.4027 . . . ; an irrational number
2.4027 . . . ; an irrational number

0.3726 . . . ; an irrational number
0.3726 . . . ; an irrational number

2.40; a rational number

Answer 1

To find the product of \( \sqrt{5} \) and \( \frac{1}{6} \), we calculate:

\[
\text{Product} = \sqrt{5} \times \frac{1}{6} = \frac{\sqrt{5}}{6}
\]

Next, we need to classify this number.

- \( \sqrt{5} \) is an irrational number.
- The product of a rational number (like \( \frac{1}{6} \)) and an irrational number (like \( \sqrt{5} \)) is also irrational.

Thus, \( \frac{\sqrt{5}}{6} \) is an irrational number.

Now, let’s find the approximate decimal value of \( \frac{\sqrt{5}}{6} \):

Calculating \( \sqrt{5} \approx 2.236 \), we can find:

\[
\frac{\sqrt{5}}{6} \approx \frac{2.236}{6} \approx 0.3726
\]

So the product \( \frac{\sqrt{5}}{6} \approx 0.3726 \ldots \) and it is an irrational number.

Validating with the response options:

- The correct answer is: **0.3726 . . . ; an irrational number**.