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!
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