To find an irrational number between \(\sqrt{14}\) and \(\sqrt{18}\), we can first determine approximate decimal values for \(\sqrt{14}\) and \(\sqrt{18}\).
- \(\sqrt{14} \approx 3.74\)
- \(\sqrt{18} \approx 4.24\)
Now, we need to evaluate the options provided:
- \(\sqrt{10} \approx 3.16\)
- \(\sqrt{13} \approx 3.61\)
- \(\sqrt{19} \approx 4.36\)
- \(\sqrt{15} \approx 3.87\)
To find a number between \(\sqrt{14}\) and \(\sqrt{18}\) (approximately between 3.74 and 4.24):
- \(\sqrt{10} \approx 3.16\) (too low)
- \(\sqrt{13} \approx 3.61\) (too low)
- \(\sqrt{19} \approx 4.36\) (too high)
- \(\sqrt{15} \approx 3.87\) (within range)
The number that is between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).
Thus, the answer is:
\(\sqrt{15}\)