To find between which whole numbers \( \sqrt{96} \) lies, we first need to calculate \( \sqrt{96} \).
We can simplify \( \sqrt{96} \): \[ \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6} \]
Next, we can find the approximate value of \( \sqrt{6} \). Since we know that \( 2.4^2 = 5.76 \) and \( 2.5^2 = 6.25 \), we can estimate that \( \sqrt{6} \) is slightly greater than \( 2.4 \) but less than \( 2.5 \).
For better accuracy, we can use a calculator to find: \[ \sqrt{6} \approx 2.449 \]
Now we multiply by 4: \[ \sqrt{96} \approx 4 \times 2.449 \approx 9.796 \]
Next, we determine where \( 9.796 \) lies on the number line in relation to whole and rational numbers. The nearest half values surrounding \( 9.796 \) are \( 9.5 \) and \( 10 \).
From this calculation, \( \sqrt{96} \) is between: \[ 9.5 \quad \text{and} \quad 10 \]
Thus, the answer is: B. 9.5 and 10