To determine which of the given options results in an integer, we need to simplify each square root.
Option a.) [tex]\(\sqrt{27}\)[/tex]
- The square root of 27 can be approximated or calculated as follows:
[tex]\[
\sqrt{27} \approx 5.196
\][/tex]
- This is not an integer.
Option b.) [tex]\(\sqrt{15}\)[/tex]
- The square root of 15 can be simplified or approximated as follows:
[tex]\[
\sqrt{15} \approx 3.873
\][/tex]
- This is not an integer.
Option c.) [tex]\(\sqrt{169}\)[/tex]
- The square root of 169 can be simplified as follows:
[tex]\[
\sqrt{169} = 13
\][/tex]
- This is an integer.
Option d.) [tex]\(\sqrt{31}\)[/tex]
- The square root of 31 can be approximated or calculated as follows:
[tex]\[
\sqrt{31} \approx 5.568
\][/tex]
- This is not an integer.
From the above simplifications, we observe that the only option resulting in an integer is:
Option c.) [tex]\(\sqrt{169}\)[/tex]
Thus, the correct answer is:
[tex]\[
\boxed{\sqrt{169}}
\][/tex]
