To find out between which whole number and rational number \( \sqrt{10} \) is situated, we first need to calculate \( \sqrt{10} \).
The approximate value of \( \sqrt{10} \) is about 3.162.
Next, we identify the whole numbers surrounding this value, which are 3 and 4.
For the nearest half, we consider values like 3, 3.5, and 4. The closest rational number to \( \sqrt{10} \) is 3.5 as it's the midpoint between 3 and 4.
Therefore, \( \sqrt{10} \) is between the whole number 3 and the rational number 3.5.
In conclusion, \( \sqrt{10} \) is between 3 (whole number) and 3.5 (rational number to the nearest half).