To find the length of the diagonal \( x \) on the bottom face of a cube with a side length of 6, we can use the formula for the diagonal of a square. The diagonal \( d \) of a square with side length \( s \) is given by the formula:
\[ d = s\sqrt{2} \]
In this case, the side length \( s \) is 6. Plugging this into the formula, we get:
\[ d = 6\sqrt{2} \]
Now we can calculate the numerical value of \( 6\sqrt{2} \):
\[ \sqrt{2} \approx 1.414 \] \[ d \approx 6 \times 1.414 \approx 8.485 \]
Rounding this to the nearest tenth, we find:
\[ d \approx 8.5 \]
Therefore, the length of the diagonal \( x \) is:
8.5