The tiles in a store are being compared. The diagonal of one tile is nine square root 2 cm and the other tile is eight square root of 2 cm. What is the difference in the length of the di agonal?

To find the difference in the length of the diagonals of the two tiles, we subtract the length of the diagonal of the second tile from the length of the diagonal of the first tile.

The diagonal of the first tile is \( 9\sqrt{2} \) cm and the diagonal of the second tile is \( 8\sqrt{2} \) cm.

We calculate the difference as follows:

\[
9\sqrt{2} - 8\sqrt{2} = (9 - 8)\sqrt{2} = 1\sqrt{2} = \sqrt{2}
\]

Thus, the difference in the length of the diagonals of the two tiles is \( \sqrt{2} \) cm.