To determine the rational number to the nearest half for √97, we need to find the two nearest perfect squares. The perfect squares closest to 97 are 81 (9^2) and 100 (10^2).
The difference between 97 and 81 is 16, while the difference between 100 and 97 is also 16. Since 97 is closer to 100, we can assume √97 is closer to 10 than to 9.
Therefore, the rational number to the nearest half for √97 is 10.