https://file.aiquickdraw.com/mathbot/file/1726775706151d6y6ok5x.jpg

Let's analyze each statement from the image:

1. **π is irrational because π is a repeating decimal.**
   - **False**: π is irrational, but not because it's a repeating decimal. π is non-repeating and non-terminating, which makes it irrational.

2. **√7 is irrational because 7 is not a perfect square.**
   - **True**: The square root of a non-perfect square (like 7) is irrational. Perfect squares, like 9 or 16, have rational square roots, but √7 does not.

3. **7.1234... is irrational because it is a nonterminating, nonrepeating decimal.**
   - **True**: Non-terminating and non-repeating decimals are the defining characteristics of irrational numbers.

4. **√7 is rational because 7 is not a perfect square.**
   - **False**: √7 is irrational, and the statement claims the opposite.

5. **π is irrational because π is not a repeating decimal.**
   - **True**: This is the correct reason why π is irrational—it's a non-terminating, non-repeating decimal.

### Correct Answers:
- Statement 2: "√7 is irrational because 7 is not a perfect square."
- Statement 3: "7.1234... is irrational because it is a nonterminating, nonrepeating decimal."
- Statement 5: "π is irrational because π is not a repeating decimal."

Let me know if you'd like further details!

### Follow-up questions:
1. Why is a non-repeating, non-terminating decimal always irrational?
2. How do perfect squares relate to the rationality of square roots?
3. Can repeating decimals ever be irrational?
4. Why is π classified as a transcendental number in addition to being irrational?
5. How does the concept of rational vs irrational numbers apply to other roots like cube roots?

### Tip:
A repeating decimal (like 1/3 = 0.333...) is always rational, while non-repeating decimals indicate irrational numbers.

Select all the statements that are true about π and √7, relating to their rationality and decimal properties.

Explore why π and √7 are classified as irrational numbers, focusing on their decimal expansion and square root properties. This problem addresses key concepts such as non-repeating, non-terminating decimals, and the definition of irrational numbers. Suitable for students in Grades 9-11.

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