Question

Which two numbers is
\sqrt{ }18 between?
4.1 and 4.2
4.2 and 4.3
4.3 and 4.4
4.4 and 4.5

Answer 1

To determine between which two numbers \(\sqrt{18}\) lies, we can calculate the approximate value of \(\sqrt{18}\).

First, we know that:
\[
\sqrt{16} = 4 \quad \text{(since } 4^2 = 16\text{)}
\]
and
\[
\sqrt{25} = 5 \quad \text{(since } 5^2 = 25\text{)}
\]

Since \(16 < 18 < 25\), we conclude that:
\[
4 < \sqrt{18} < 5
\]

Next, let's find a more precise estimate for \(\sqrt{18}\) by simplifying it:
\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\]

Using the approximate value:
\[
\sqrt{2} \approx 1.414
\]
Thus:
\[
\sqrt{18} \approx 3 \times 1.414 \approx 4.242
\]

Now we can check where \(4.242\) lies by comparing it with the given intervals:
- \(4.1\) and \(4.2\) (too low)
- \(4.2\) and \(4.3\) (fits)
- \(4.3\) and \(4.4\) (too high)

Therefore, \(\sqrt{18}\) is between \(4.2\) and \(4.3\).

The correct answer is:
**4.2 and 4.3**.