The problem asks us to identify which of the given numbers is an irrational number. The options are 14, 0, 5/2, and $\sqrt{7}$.

1. Problem Description

The problem asks us to identify which of the given numbers is an irrational number. The options are 14, 0, 5/2, and $\sqrt{7}$.

2. Solution Steps

An irrational number is a number that cannot be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is not zero. In other words, it is a real number that is not a rational number.

(1) 14 can be written as $\frac{14}{1}$, so it is a rational number.

(2) 0 can be written as $\frac{0}{1}$, so it is a rational number.

(3) $\frac{5}{2}$ is already in the form of a fraction of two integers, so it is a rational number.

(4) $\sqrt{7}$ is an irrational number. The square root of a non-perfect square is irrational. 7 is not a perfect square (i.e., there is no integer $n$ such that $n^2 = 7$).

3. Final Answer

$\sqrt{7}$