When is the rational? predicate useful if even (rational? (sqrt 2)) is true?
I understand that the matter of qualifying numbers rational/irrational is complicated by the fact that numbers are inexactly represented. The predicate is there, anyway.
In an implementation that uses floating point representation of mathematically irrational numbers, any number other than infinity or NaN will be be rational, since a floating point value is essentially a fraction with a power of 2 as the denominator. Basically, irrational numbers like π and (sqrt 2) are actually rational approximations in these systems.
The rational? predicate is provided for completeness to allow for other possible representations of irrational numbers, such as continued fractions. I don't think there are any real implementations like this, it's just theoretical.
The rational? predicate returns true if a number is a rational: a number of the form n/m where n and m are integers and m is not zero. That means that, as Barmar says, it must return true for floats (assuming the normal float representation), because floats are, in fact rationals.
But there's a really important case where rational? must return false: complex numbers. Complex numbers are not rational numbers. So for any implementation which has complex numbers, rational? will return false for those:
> (rational? 1+2i)
#f
> (number? 1+2i)
#t
> (complex? 1+2i)
#t
> (real? 1+2i)
#f
> (exact? 1+2i)
#t
> (complex? 1)
#t
> (rational? 1+0i)
#t