Final answer:
The expression z/√(x²-y²) is not necessarily a rational number. It depends on the values of x, y, and z. If x²-y² is a perfect square, then the expression is rational.
Step-by-step explanation:
The expression z/√(x²-y²) is not necessarily a rational number. This is because the square root √(x²-y²) can be irrational depending on the values of x and y. If x²-y² is a perfect square, then the square root will be rational and the expression z/√(x²-y²) will also be rational. However, if x²-y² is not a perfect square, then the square root will be irrational and the expression will not be rational.
For example, if x=3, y=2, and z=4, we have √(x²-y²) = √(3²-2²) = √5, which is irrational. Therefore, z/√(x²-y²) = 4/√5 is also irrational.
So, in general, the rationality of z/√(x²-y²) depends on the values of x, y, and z.