Question

Which irrational number is between the square root of14 and the square root of18? (1 point)

•the square root of 13
•the square root of 15
•the square root of 19
•the square root of 10

Answer 1

To find an irrational number between \(\sqrt{14}\) and \(\sqrt{18}\), we can first approximate the square roots of these numbers:

\[
\sqrt{14} \approx 3.74 \quad \text{(since \(3.74^2 \approx 13.88\) and \(3.75^2 = 14.0625\))}
\]
\[
\sqrt{18} \approx 4.24 \quad \text{(since \(4.24^2 \approx 17.98\) and \(4.25^2 = 18.0625\))}
\]

Now, we need to determine which of the given options falls between these two values:

1. **\(\sqrt{13}\)**:
\[
\sqrt{13} \approx 3.61 \quad \text{(which is less than \(3.74\))}
\]

2. **\(\sqrt{15}\)**:
\[
\sqrt{15} \approx 3.87 \quad \text{(which is between \(3.74\) and \(4.24\))}
\]

3. **\(\sqrt{19}\)**:
\[
\sqrt{19} \approx 4.36 \quad \text{(which is greater than \(4.24\))}
\]

4. **\(\sqrt{10}\)**:
\[
\sqrt{10} \approx 3.16 \quad \text{(which is less than \(3.74\))}
\]

The only option that lies between \(\sqrt{14}\) and \(\sqrt{18}\) is:

\(\sqrt{15}\)

So, the answer is **the square root of 15**.