Question

Which irrational number is between √14 and √18

√15

√13

√10

√19

Answer 1

To determine which of the given options is an irrational number that falls between \( \sqrt{14} \) and \( \sqrt{18} \), we can evaluate each option:

1. **Calculating \( \sqrt{14} \) and \( \sqrt{18} \):**
- \( \sqrt{14} \) is approximately \( 3.74 \).
- \( \sqrt{18} \) is approximately \( 4.24 \).

Now, let's check the options:

2. **Checking \( \sqrt{15} \):**
- \( \sqrt{15} \) is approximately \( 3.87 \).
- Since \( 3.74 < 3.87 < 4.24 \), \( \sqrt{15} \) is between \( \sqrt{14} \) and \( \sqrt{18} \).

3. **Checking \( \sqrt{13} \):**
- \( \sqrt{13} \) is approximately \( 3.61 \).
- Since \( 3.61 < 3.74 \), it's not between \( \sqrt{14} \) and \( \sqrt{18} \).

4. **Checking \( \sqrt{10} \):**
- \( \sqrt{10} \) is approximately \( 3.16 \).
- Since \( 3.16 < 3.74 \), it's not between \( \sqrt{14} \) and \( \sqrt{18} \).

5. **Checking \( \sqrt{19} \):**
- \( \sqrt{19} \) is approximately \( 4.36 \).
- Since \( 4.36 > 4.24 \), it's not between \( \sqrt{14} \) and \( \sqrt{18} \).

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

**\( \sqrt{15} \)**.