https://file.aiquickdraw.com/mathbot/file/1729051471860f9b9alxy.jpg

Let's determine whether each number is rational or irrational based on the image.

1. **√11**: 
   - This is an **irrational number** because the square root of 11 cannot be expressed as a fraction of two integers, and its decimal form is non-terminating and non-repeating.

2. **1/11**: 
   - This is a **rational number** because it is a fraction of two integers (1 and 11).

3. **0.1̅ (repeating decimal)**:
   - This is a **rational number** because repeating decimals can always be expressed as a fraction of two integers.

4. **√111**: 
   - This is an **irrational number** because the square root of 111 cannot be expressed as a fraction, and its decimal form is non-terminating and non-repeating.

### Summary:
- **√11**: Irrational
- **1/11**: Rational
- **0.1̅**: Rational
- **√111**: Irrational

Would you like a more detailed explanation for any of these numbers?

Here are 5 related questions:
1. Why are square roots of non-perfect squares irrational?
2. Can a repeating decimal ever be irrational?
3. What is the difference between terminating and repeating decimals?
4. How can we prove a number is rational?
5. Are all fractions rational numbers?

**Tip:** If a decimal terminates or repeats, it's a rational number!

Determine whether each number is rational or irrational.

Learn how to determine whether numbers like √11, 1/11, repeating decimals, and √111 are rational or irrational. This problem covers key concepts of rational and irrational numbers, repeating decimals, and square roots. Suitable for Grades 6-8.

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