Question

Using a number line, what whole number and rational number to the nearest half is 97−−√ between?(1 point)
97−−√ is between and .

Answer 1

Thatswrong

Answer 2

To find the whole number and the rational number to the nearest half that \( \sqrt{97} \) is between, we first calculate \( \sqrt{97} \).

1. **Whole Number:**
- We know that \( 9^2 = 81 \) and \( 10^2 = 100 \). Since \( 97 \) is between \( 81 \) and \( 100 \), we have:
\[
9 < \sqrt{97} < 10
\]
Thus, the whole number is \( 9 \).

2. **Rational Number to the Nearest Half:**
- Next, we can approximate \( \sqrt{97} \). By calculating:
\[
\sqrt{97} \approx 9.8
\]
To the nearest half, \( 9.8 \) is closer to \( 9.5 \) than to \( 10.0 \).

Combining both results, we find that:
\[
\sqrt{97} \text{ is between } 9 \text{ and } 9.5.
\]

So, \(\sqrt{97}\) is between \(9\) and \(9.5\).

Answer 3

Let’s re-evaluate the calculation for \( \sqrt{97} \) to ensure we find the correct whole number and rational number.

1. **Whole Number:**
- As established before, \( 9^2 = 81 \) and \( 10^2 = 100 \).
- Therefore, since \( 97 \) is between \( 81 \) and \( 100 \), we have:
\[
9 < \sqrt{97} < 10
\]
Thus, \( 9 \) is indeed the lower whole number.

2. **More Accurate Approximation of \( \sqrt{97} \):**
- Let's compute \( \sqrt{97} \) using a calculator:
\[
\sqrt{97} \approx 9.8489
\]
- Rounding this to the nearest half, we get \( 9.5 \) because \( 9.8489 \) is closer to \( 9.5 \) than to \( 10 \).

Thus, \( \sqrt{97} \) is indeed between:

- Whole number: \( 9 \)
- Rational number to the nearest half: \( 9.5 \)

So the correct statement is:
\[
\sqrt{97} \text{ is between } 9 \text{ and } 9.5.
\]

If your question asked for something different, please clarify, and I’d be happy to assist!