To determine which number is irrational, let's analyze each option:

1. A) $\sqrt{2}$: This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating (approximately 1.414213...).

2. B) $\frac{1}{2}$: This is a rational number, as it can be expressed as the fraction $\frac{1}{2}$, where both the numerator and denominator are integers.

3. C) 0.4: This is a rational number because it can be expressed as the fraction $\frac{2}{5}$.

4. D) 1.\overline{5}: This is also a rational number, as it represents a repeating decimal and can be written as $\frac{5}{3}$.

The correct answer is A) $\sqrt{2}$, which is irrational.

Would you like more details or have any questions?

Here are some related questions:

1. What is an irrational number?
2. Can all square roots be considered irrational numbers?
3. How can you identify a rational number?
4. What is the difference between a repeating decimal and a non-repeating decimal?
5. Are all non-terminating decimals irrational?

Tip: An irrational number cannot be expressed exactly as a simple fraction and has a decimal expansion that goes on forever without repeating.