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

Question

Responses

0.3726 . . . ; an irrational number
0.3726 . . . ; an irrational number
2.4027 . . . ; an irrational number
2.4027 . . . ; an irrational number
2.40; a rational number
2.40; a rational number
0.37; a rational number

Answer 1

To find the product of √5 and 1/6, we multiply them together:

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

Now, we need to consider the nature of this number. Since √5 is an irrational number (it cannot be expressed as a fraction of two integers), and the product of an irrational number and a non-zero rational number (in this case, 1/6) is also irrational.

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

Now, let's estimate the value of \(\sqrt{5}\):

\(\sqrt{5} \approx 2.236\)

So,

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

This provides us with a rough estimate of the product.

Considering the answers provided, the most suitable response is:

0.3726 . . . ; an irrational number