To find the length of the diagonal of a cube, we can use the formula for the space diagonal \( d \) of a cube given its edge length \( a \):
\[ d = a \sqrt{3} \]
In your case, the edge length \( a \) is 8 inches. Plugging this value into the formula:
\[ d = 8 \sqrt{3} \]
Now, we calculate \( \sqrt{3} \):
\[ \sqrt{3} \approx 1.732 \]
Now substitute back into the equation:
\[ d \approx 8 \times 1.732 \approx 13.856 \]
Rounding \( 13.856 \) to the nearest tenth gives:
\[ d \approx 13.9 , \text{in.} \]
Thus, the length of the diagonal of the cube is approximately 13.9 in.