To find the whole number and the rational number to the nearest half that \( V 40 \) is between, let's first calculate \( V 40 \):
\[ V 40 = \sqrt{40} \approx 6.3246 \]
Now, examining the whole number:
- The whole numbers surrounding \( 6.3246 \) are \( 6 \) and \( 7 \).
- Therefore, \( V 40 \) is between \( 6 \) and \( 7 \).
Next, we determine the rational number to the nearest half:
- The nearest halves around \( 6.3246 \) are \( 6.0 \) and \( 6.5 \).
- Since \( 6.3246 \) is closer to \( 6.5 \) than to \( 6.0 \), we round \( 6.3246 \) to \( 6.5 \).
Thus, we can conclude that:
\[ V 40 \text{ is between } 6 \text{ and } 7 \text{, and between } 6 \text{ and } 6.5. \]
Final answer:
V 40 is between 6 and 7, and 6 and 6.5.