Question

Which irrational number is between square root 14 and square root 18?

square root 19
square root 10
square root 13
square root 15

Answer 1

To find an irrational number that lies between \(\sqrt{14}\) and \(\sqrt{18}\), we need to evaluate the approximate values of these square roots:

\[
\sqrt{14} \approx 3.74
\]
\[
\sqrt{18} \approx 4.24
\]

Now we will evaluate the candidates given:

1. \(\sqrt{19} \approx 4.36\) (this is greater than \(\sqrt{18}\))
2. \(\sqrt{10} \approx 3.16\) (this is less than \(\sqrt{14}\))
3. \(\sqrt{13} \approx 3.61\) (this is also less than \(\sqrt{14}\))
4. \(\sqrt{15} \approx 3.87\) (this is between \(\sqrt{14}\) and \(\sqrt{18}\))

The only candidate that falls between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).

Therefore, the irrational number that is between \(\sqrt{14}\) and \(\sqrt{18}\) is:

\[
\sqrt{15}
\]