Question

Using a number line, what whole number and rational number to the nearest half is 20−−√ between?(1 point) show you work botty

Answer 1

To find the whole number and the rational number (to the nearest half) that \( \sqrt{20} \) falls between, let's first compute the value of \( \sqrt{20} \).

### Step 1: Calculate \( \sqrt{20} \)

We know that:

\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

Now to find a decimal approximation of \( \sqrt{5} \), we can use a calculator or approximate it. The value of \( \sqrt{5} \) is approximately \( 2.236 \).

Then,

\[
\sqrt{20} \approx 2 \times 2.236 \approx 4.472
\]

### Step 2: Determine whole numbers around \( \sqrt{20} \)

We can see that \( 4.472 \) is between the whole numbers \( 4 \) and \( 5 \).

### Step 3: Find the rational number to the nearest half

To find the nearest half, we can round \( 4.472 \) to the nearest half unit. The nearest halves to \( 4.472 \) are:

- \( 4.0 \)
- \( 4.5 \)
- \( 5.0 \)

Since \( 4.472 \) is closer to \( 4.5 \) than to \( 4.0 \), we consider \( 4.5 \) as the nearest half.

### Conclusion

Thus, \( \sqrt{20} \) is between:

- Whole number: \( 4 \) and \( 5 \)
- Nearest half: \( 4.5 \)

So, \( \sqrt{20} \) is between the whole number \( 4 \) and the rational number \( 4.5 \).