Arectangle has a length of 8 inches. the area of the rectangle, in square inches, is an irrational number. the width of the rectangle must be

The width must be irrational

If you multiply a rational and irrational number together, the result is irrational. The length 8 is rational. The area is told to be irrational. This forces the width to be irrational. If the width were rational, then

rational*rational = rational

but the area was irrational. So this is a contradiction.