To find the value of \( \sqrt{97} \) and determine which whole numbers and rational numbers (to the nearest half) it is between, let's first calculate \( \sqrt{97} \).
The square roots of perfect squares around 97 are:
- \( 9^2 = 81 \)
- \( 10^2 = 100 \)
This shows that \( 9 < \sqrt{97} < 10 \).
Now, to refine our estimate, let's calculate \( \sqrt{97} \) more precisely. Using a calculator, we find:
\[ \sqrt{97} \approx 9.8489 \]
Now, to identify the whole number and rational number to the nearest half, we can see:
- The whole number is \( 9 \) (since \( 9 < 9.8489 < 10 \)).
- The closest rational number to the nearest half around \( 9.8489 \) are \( 9.5 \) and \( 10 \), and since \( 9.8489 \) is closer to \( 10 \), we consider \( 10 \) as the upper boundary.
Thus, \( \sqrt{97} \) is between \( 9 \) and \( 10 \).
So the answer is:
\[ \sqrt{97} \text{ is between } 9 \text{ and } 10. \]