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To determine which of the following numbers is irrational, let's examine the options carefully:

1. **2.25 (with bar notation over 25)**: This number represents a repeating decimal, \(2.252525...\), which is a rational number since it can be expressed as a fraction (in this case, \( \frac{223}{99} \)).

2. **2.24**: This is a terminating decimal, and any terminating decimal is rational because it can be written as a fraction (in this case, \( \frac{224}{100} \)).

3. **2.2 (with bar notation over 2)**: This represents a repeating decimal, \(2.222...\), which is also rational, as it can be written as a fraction \( \frac{20}{9} \).

4. **\(\sqrt{5}\)**: This is an irrational number because the square root of 5 cannot be expressed as a simple fraction, and its decimal expansion is non-repeating and non-terminating.

So, the **irrational number** between 2.2 and 2.4 is **\(\sqrt{5}\)**.

Would you like more details or explanations?

Here are 5 related questions:
1. What makes a number irrational?
2. Can repeating decimals ever be irrational?
3. How do you convert repeating decimals into fractions?
4. What is the approximate value of \(\sqrt{5}\)?
5. Are all square roots irrational?

**Tip:** Irrational numbers cannot be written as exact fractions and their decimal expansion goes on infinitely without repeating.

Which of the following is an irrational number between 2.2 and 2.4?

Learn how to identify an irrational number between 2.2 and 2.4. This problem explores the difference between rational and irrational numbers, focusing on square roots and decimal expansions. Suitable for students in Grades 6-8.

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