To determine the whole number and rational number to the nearest half that \( \sqrt{97} \) is between, we first need to calculate its approximate value.
Calculating \( \sqrt{97} \):
The square roots of numbers close to 97 are:
- \( 9^2 = 81 \)
- \( 10^2 = 100 \)
This indicates that \( 9 < \sqrt{97} < 10 \).
Next, we can get a more precise estimate. The approximate value of \( \sqrt{97} \) can be calculated using a calculator, which gives \( \sqrt{97} \approx 9.848 \).
Now, let's find the nearest half. The nearby halves are:
- \( 9.5 \)
- \( 10.0 \)
Since \( 9.848 \) is closer to \( 10 \), the rational number to the nearest half is \( 10.0 \).
Thus, \( \sqrt{97} \) is between:
- Whole number: \( 9 \) (the lower bound)
- Rational number to the nearest half: \( 10 \)
Final answer: \( \sqrt{97} \) is between 9 and 10.
1 answer