Question

Find the product of 5–√
and 16
. What type of number is it?(1 point)
Responses

0.37; a rational number
0.37; a rational number

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

2.40; a rational number
2.40; a rational number

2.4027 . . . ; an irrational number

Answer 1

To find the product of \( 5 - \sqrt{5} \) and \( 16 \), we first multiply:

\[
(5 - \sqrt{5}) \times 16 = 80 - 16\sqrt{5}
\]

Next, we will analyze the nature of the number \( 80 - 16\sqrt{5} \).

- \( 80 \) is a rational number.
- \( 16\sqrt{5} \) involves \( \sqrt{5} \), which is an irrational number.

Since the product results in a rational number minus an irrational number, the outcome is an irrational number.

Thus, the product \( 80 - 16\sqrt{5} \) is an irrational number.

None of the given responses directly match \( 80 - 16\sqrt{5} \), but it can be concluded that the appropriate answer related to irrational results would be "2.4027... ; an irrational number" since it indicates an irrational result. However, please note that without specific numerical values calculated, this is an inference.

The product is an irrational number.