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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.

¿Qué número es irracional?
A) √2 
B) 1/2 
C) 0,4 
D) 1,5

Learn how to identify irrational numbers with this detailed example, featuring √2 as an irrational number. Understand the difference between rational and irrational numbers using various options, such as 1/2, 0.4, and repeating decimals. Suitable for students in Grades 7-9.

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