Question

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

Answer 1

To determine the whole number and rational number to the nearest half that \(\sqrt{97}\) is between, we first need to estimate its value.

Calculating \( \sqrt{97} \):

1. **Find perfect squares near 97**:
- \(9^2 = 81\)
- \(10^2 = 100\)

So, we know that:
\[
9 < \sqrt{97} < 10
\]

2. **Estimate \(\sqrt{97}\)**:
- To get a more precise estimate, calculate \((9.8)^2\) and \((9.9)^2\):
- \(9.8^2 = 96.04\)
- \(9.9^2 = 98.01\)

This implies:
\[
9.8 < \sqrt{97} < 9.9
\]

3. **Finding the nearest half**:
- The nearest halves around this interval are \(9.5\) and \(10\).
- Since \(9.8\) is closer to \(9.5\) than \(10\), we will choose \(9.5\).

4. **Identify whole numbers and rational numbers**:
- The whole numbers directly below and above \( \sqrt{97} \) are \(9\) and \(10\).
- The rational number to the nearest half is \(9.5\).

Therefore, \(\sqrt{97}\) is between:
- Whole number: **9 and 10**
- Rational number to the nearest half: **9.5**