Which irrational number is between 14−−√ and 18−−√ ?(1 point)

Answer 1

To find an irrational number that lies between \(\sqrt{14}\) and \(\sqrt{18}\), we first need to approximate the values of \(\sqrt{14}\) and \(\sqrt{18}\).

1. \(\sqrt{14} \approx 3.74\)
2. \(\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \approx 3 \cdot 1.41 \approx 4.24\)

Now we see that \(\sqrt{14} \approx 3.74\) and \(\sqrt{18} \approx 4.24\). Therefore, we are looking for an irrational number between approximately 3.74 and 4.24.

One option for an irrational number in this range is \(\sqrt{15}\), since:

\[ \sqrt{14} < \sqrt{15} < \sqrt{18} \]

Calculating \(\sqrt{15}\):

\(\sqrt{15} \approx 3.87\).

Thus, \(\sqrt{15}\) is indeed between \(\sqrt{14}\) and \(\sqrt{18}\).

So, a suitable irrational number between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).