To find what whole number and rational number to the nearest half \( \sqrt{10} \) is between, we first need to approximate \( \sqrt{10} \).
Calculating \( \sqrt{10} \):
- We know that \( 3^2 = 9 \) and \( 4^2 = 16 \). Therefore, \( \sqrt{10} \) is between 3 and 4.
- To be more precise, we can estimate by checking halfway points:
- \( 3.1^2 = 9.61 \)
- \( 3.2^2 = 10.24 \)
From this, we see that:
- \( \sqrt{10} \) is between 3.1 and 3.2.
Next, let’s check for a rational number to the nearest half:
- The nearest half numbers between 3 and 4 are 3.0, 3.5, and 4.0.
- Since \( \sqrt{10} \) is approximately 3.16, it rounds to 3.0 or 3.5.
Thus, we can determine:
\[ \sqrt{10} \text{ is between } 3 \text{ and } 3.5. \]
So in conclusion:
\(\sqrt{10}\) is between 3 (whole number) and 3.5 (rational number to the nearest half).
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