To determine which of the given choices results in an integer, let's analyze the square roots of each option.
1. Option a: [tex]\( \sqrt{27} \)[/tex]
[tex]\[\sqrt{27} \approx 5.196\][/tex]
This is not an integer.
2. Option b: [tex]\( \sqrt{31} \)[/tex]
[tex]\[\sqrt{31} \approx 5.568\][/tex]
This is not an integer.
3. Option c: [tex]\( \sqrt{169} \)[/tex]
[tex]\[\sqrt{169} = 13\][/tex]
This is an integer.
4. Option d: [tex]\( \sqrt{15} \)[/tex]
[tex]\[\sqrt{15} \approx 3.873\][/tex]
This is not an integer.
Thus, the square root of 169 is the only value that results in an integer. Therefore, the correct answer is:
c.) [tex]\( \sqrt{169} \)[/tex]
