Question

Which irrational number is between sqrt(14) and sqrt(18) ? (1 point) sqrt(13); sqrt(10) < sqrt(10); sqrt(15)

Answer 1

To find an irrational number between \(\sqrt{14}\) and \(\sqrt{18}\), we can start by analyzing these two square roots:

1. Calculate the approximate decimal values:
- \(\sqrt{14} \approx 3.74\)
- \(\sqrt{18} \approx 4.24\)

This means we are looking for an irrational number between approximately \(3.74\) and \(4.24\).

Next, let's evaluate the options given:

- \(\sqrt{13} \approx 3.61\) (not between \(3.74\) and \(4.24\))
- \(\sqrt{10} \approx 3.16\) (not between \(3.74\) and \(4.24\))
- \(\sqrt{15} \approx 3.87\) (this is between \(3.74\) and \(4.24\))

Since \(\sqrt{15}\) is approximately \(3.87\) and lies between \(\sqrt{14}\) and \(\sqrt{18}\), the answer is:

\(\sqrt{15}\)