To determine where \(\sqrt{96}\) lies on a number line, we first need to find the approximate value of \(\sqrt{96}\).
Calculating \(\sqrt{96}\):
\[ \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6} \]
Now we need to approximate \(\sqrt{6}\). Knowing that:
\[ \sqrt{4} = 2 \text{ and } \sqrt{9} = 3, \]
we estimate \(\sqrt{6}\) to be between 2 and 3. A more refined estimation gives:
\[ \sqrt{6} \approx 2.45. \]
So, we can compute:
\[ 4 \times 2.45 = 9.8. \]
Thus, \(\sqrt{96} \approx 9.8\).
Next, we round \(\sqrt{96}\) to the nearest half:
\[ 9.8 \text{ rounds to } 10. \]
Thus, \(\sqrt{96}\) is between 9.5 and 10. Therefore, the correct answer is:
B. 9.5 and 10.
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