False: Justification

Definition of Irrational Numbers:
- Irrational numbers are numbers that cannot be expressed as a simple fraction or ratio of two integers. They are non-repeating and non-terminating decimals.

Square of Irrational Numbers:
- When an irrational number is squared, the result may or may not be rational.
- For example, the square of √2 is 2, which is a rational number.
- However, the square of √3 is 3, which is also irrational.

Counterexample:
- Consider the square root of 2 (√2), which is an irrational number.
- When squared, (√2)^2 = 2, which is a rational number.
- This shows that the square of an irrational number can result in a rational number.

Conclusion:
- The statement that the square of an irrational number is always rational is false.
- There are cases where the square of an irrational number results in a rational number, but there are also cases where it remains irrational.
- Therefore, the square of an irrational number can be rational or irrational, depending on the specific number being squared.