https://file.aiquickdraw.com/mathbot/file/1726241001576wi0mjg2l.jpg

Let's evaluate the numbers in the list to identify which one(s) are irrational:

1. **√64**: The square root of 64 is 8, a whole number. Hence, it's a **rational number**.

2. **1/64**: This is a fraction, which is a ratio of two integers. Therefore, it is a **rational number**.

3. **√3**: The square root of 3 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating. Therefore, it is an **irrational number**.

4. **√28**: This simplifies to √(4 × 7) = 2√7. Since √7 is irrational, √28 is also an **irrational number**.

5. **√4**: The square root of 4 is 2, a whole number. Hence, it's a **rational number**.

6. **23.157**: This is a terminating decimal, so it can be expressed as a fraction (23157/1000). Therefore, it is a **rational number**.

7. **-64**: This is an integer, which can be written as a fraction (-64/1), so it is a **rational number**.

### Conclusion:
The irrational numbers in the list are:
- **√3**
- **√28**

Would you like more details on this explanation, or have any questions?

### Relative Questions:
1. What is the difference between rational and irrational numbers?
2. How do you simplify square roots like √28 into more manageable forms?
3. Why are terminating and repeating decimals considered rational numbers?
4. What are some real-life examples where irrational numbers are used?
5. How do you prove whether a number is irrational?

### Tip:
When working with square roots, simplify them whenever possible to better identify if the result is rational or irrational.

Which number in the list is/are an irrational number?
1. √64
2. 1/64
3. √3
4. √28
5. √4
6. 23.157
7. -64

Learn how to identify irrational numbers from a list including square roots and decimals. This problem covers key mathematical concepts such as rational and irrational numbers and the simplification of square roots. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation