Final answer:
Among the expressions given, (b) x²/p represents a rational number, which simplifies to 1 because x² is the same as p for a prime number p greater than 2000.
Step-by-step explanation:
The student asks to evaluate which of the given expressions represents a rational number if 'p' is a prime number greater than 2000 and 'x' is the square root of 'p' (x = √p). To be a rational number, the expression must equal a fraction where both the numerator and the denominator are integers and the denominator is not zero.
Looking at option (a), p/x, we can rewrite it as p·(1/√p), which simplifies to √p. Since 'p' is prime and larger than 2000, √p is not an integer, so (a) is not rational.
Option (b), x²/p, becomes p/p, since x² is the same as p (√p times itself). This expression does indeed represent a rational number because p/p simplifies to 1, which is a rational number.
For option (c), x/p, we get √p/p, which is not rational since √p is not an integer and thereby the expression does not represent a ratio of two integers.
Lastly, option (d), p²/x, rewrites as p²/√p, simplifying to p·√p, which equals to p·p, and is indeed an integer but not rational as it does not have a non-zero integer denominator.
In conclusion, the expression which represents a rational number from the given options is (b) x²/p.