To compare [tex]\(\sqrt{130}\)[/tex] and [tex]\(\frac{111}{8}\)[/tex], we need to determine their numerical values and then directly compare them.
1. First, calculate the value of [tex]\(\sqrt{130}\)[/tex]:
[tex]\[
\sqrt{130} \approx 11.40175425099138
\][/tex]
2. Next, calculate the value of [tex]\(\frac{111}{8}\)[/tex]:
[tex]\[
\frac{111}{8} = 13.875
\][/tex]
3. Now, compare the two values:
[tex]\[
11.40175425099138 < 13.875
\][/tex]
Therefore, the correct comparison is:
[tex]\[
\sqrt{130} < \frac{111}{8}
\][/tex]
Hence, the correct statement is:
[tex]\[
\frac{111}{8} > \sqrt{130}
\][/tex]
