Question

Which irrational number is between square root 14 and square root 18 would the answer be square root 19 square root 13 square root 15 or square square root 10

Answer 1

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

1. **Calculate \(\sqrt{14}\)**:
\(\sqrt{14} \approx 3.74\)

2. **Calculate \(\sqrt{18}\)**:
\(\sqrt{18} \approx 4.24\)

Now, we look for an irrational number between these two values. Let's evaluate the options given:

- **\(\sqrt{19}\)**:
\(\sqrt{19} \approx 4.36\) (not between \(\sqrt{14}\) and \(\sqrt{18}\))

- **\(\sqrt{13}\)**:
\(\sqrt{13} \approx 3.61\) (not between \(\sqrt{14}\) and \(\sqrt{18}\))

- **\(\sqrt{15}\)**:
\(\sqrt{15} \approx 3.87\) (this is between \(\sqrt{14}\) and \(\sqrt{18}\))

- **\(\sqrt{10}\)**:
\(\sqrt{10} \approx 3.16\) (not between \(\sqrt{14}\) and \(\sqrt{18}\))

From the given options, \(\sqrt{15}\) is the only irrational number that lies between \(\sqrt{14}\) and \(\sqrt{18}\).