To find which irrational number lies between \(\sqrt{14}\) and \(\sqrt{18}\), we first need to approximate the values of these square roots.
- \(\sqrt{14} \approx 3.74\)
- \(\sqrt{18} \approx 4.24\)
Now let's approximate the square roots of the response options:
- \(\sqrt{10} \approx 3.16\)
- \(\sqrt{15} \approx 3.87\)
- \(\sqrt{13} \approx 3.61\)
- \(\sqrt{19} \approx 4.36\)
Now we can determine which of these values is between \(\sqrt{14} \approx 3.74\) and \(\sqrt{18} \approx 4.24\):
- \(\sqrt{10} \approx 3.16\) (not between)
- \(\sqrt{15} \approx 3.87\) (between)
- \(\sqrt{13} \approx 3.61\) (not between)
- \(\sqrt{19} \approx 4.36\) (not between)
Thus, the irrational number that is between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).