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
2.4027 . . . ; an irrational number

Answer 1

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

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

Next, we analyze the expression \( 80 - 16\sqrt{5} \):

- The term \( 80 \) is a rational number.
- The term \( 16\sqrt{5} \) involves \( \sqrt{5} \), which is an irrational number. Thus, \( 16\sqrt{5} \) is also irrational.
- The subtraction of an irrational number (\( 16\sqrt{5} \)) from a rational number (\( 80 \)) results in an irrational number.

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

Now we can provide the response in accordance with the given answer choices.

It's important to note that we should calculate \( 80 - 16\sqrt{5} \) to find a decimal approximation, but since the exact form already concluded it was irrational, we can summarize:

The final answer is:
**80 - 16√5; an irrational number.**

Since this form does not match any listed options explicitly, I suggest you use the number as an approximate decimal:

While \( 16\sqrt{5} \approx 35.777 \), we find:

\[
80 - 16\sqrt{5} \approx 80 - 35.777 = 44.223.
\]

However, the options indicated select deceitfully or misinterpret the depicted approximation.

Given those options, the conclusion of "an irrational number" with \( 0.3726...\) or \( 2.40 \) would suggest a comparison to an incorrect choice.

If you need further help or specific comparisons related to values, please request!