To determine the whole number and the rational number to the nearest half that the value of \( \sqrt{10} \) (10 to the power of 1/2 or the square root of 10) lies between, we first need to estimate \( \sqrt{10} \).
The square root of 9 is 3, and the square root of 16 is 4. Therefore:
\[ 3 < \sqrt{10} < 4 \]
To find a more precise estimate, we can calculate \( \sqrt{10} \):
\[ \sqrt{10} \approx 3.162 \]
Since this value is approximately 3.162, we can identify the whole number it lies between:
- The whole number is 3.
Next, to find the nearest half, we look at the numbers 3 and 3.5:
- Since 3.162 is closer to 3.0 than to 3.5, rounding to the nearest half gives us 3.0.
So, the final answer is:
- Whole number: 3
- Rational number to the nearest half: 3.0
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