Question

Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point) 40−−√ is between and .

Answer 1

simplify without the |{} things

Answer 2

To determine the values that \(\sqrt{40}\) is between, we start by calculating \(\sqrt{40}\).

1. **Estimate \(\sqrt{40}\):**
- We know that \(6^2 = 36\) and \(7^2 = 49\), so:
\[
6 < \sqrt{40} < 7
\]

2. **Find a more precise decimal value:**
- We can simplify \(\sqrt{40}\):
\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10}
\]

- The approximate value of \(\sqrt{10}\) is about \(3.162\), so:
\[
\sqrt{40} \approx 2 \times 3.162 \approx 6.324
\]

3. **Rounding to the nearest half:**
- The number \(6.324\) is closer to \(6.5\) than to \(6.0\), so:
\[
\sqrt{40} \approx 6.5 \text{ (to the nearest half)}
\]

4. **Determine the whole numbers and rational numbers:**
- The whole number it is between is \(6\) and \(7\).
- The rational number to the nearest half is \(6.5\).

Thus, the final answer is:
\[
\sqrt{40} \text{ is between } 6 \text{ and } 7, \text{ and the rational number to the nearest half is } 6.5.
\]