Sure! Let's analyze each option to determine which one is a rational number.
A. [tex]\(\sqrt{15}\)[/tex]:
The square root of 15 is not a perfect square, so [tex]\(\sqrt{15}\)[/tex] is an irrational number. This means it cannot be expressed as a ratio of two integers.
B. [tex]\(2.6457513110 \ldots\)[/tex]:
This number is a non-terminating, non-repeating decimal, which means it is an irrational number. It cannot be expressed as a ratio of two integers.
C. 17,156:
17,156 is an integer. Any integer is a rational number because it can be expressed as a ratio of two integers. For example, 17,156 can be written as [tex]\(\frac{17156}{1}\)[/tex]. Therefore, 17,156 is a rational number.
D. [tex]\(\sqrt{85}\)[/tex]:
The square root of 85 is not a perfect square, so [tex]\(\sqrt{85}\)[/tex] is an irrational number. It cannot be expressed as a ratio of two integers.
From this analysis, we conclude that the correct answer is:
C. 17,156
