https://file.aiquickdraw.com/mathbot/file/1726302931378xs6yv43r.jpg

The question asks, "Which of the given number sets contains all integer numbers?"

Let's examine each option to see which set contains only integers:

1. **Option 1:** \( \{\sqrt{4}, -\frac{1}{6}, 9.5\} \)
   - \( \sqrt{4} = 2 \) (an integer).
   - \( -\frac{1}{6} \) is a fraction, **not** an integer.
   - \( 9.5 \) is a decimal, **not** an integer.
   - So, **this set does not contain all integers**.

2. **Option 2:** \( \{\sqrt{49}, -1, 0\} \)
   - \( \sqrt{49} = 7 \) (an integer).
   - \( -1 \) is an integer.
   - \( 0 \) is an integer.
   - So, **this set contains all integers**.

3. **Option 3:** \( \left\{\frac{10}{4}, 13, \sqrt{20}\right\} \)
   - \( \frac{10}{4} = 2.5 \), **not** an integer.
   - \( 13 \) is an integer.
   - \( \sqrt{20} \) is an irrational number, **not** an integer.
   - So, **this set does not contain all integers**.

4. **Option 4:** \( \{-5, \sqrt{0}, \pi\} \)
   - \( -5 \) is an integer.
   - \( \sqrt{0} = 0 \), which is an integer.
   - \( \pi \) is an irrational number, **not** an integer.
   - So, **this set does not contain all integers**.

### Conclusion:
**Option 2** \( \{\sqrt{49}, -1, 0\} \) is the correct answer because it contains all integer numbers.

Do you want more details or have any questions?

Here are 5 related questions:
1. What are the properties of integer numbers?
2. How do you identify irrational numbers in a set?
3. What makes a number an integer?
4. Why isn't \( \pi \) considered an integer?
5. Can a decimal number ever be an integer?

**Tip:** Integers include positive and negative whole numbers, including zero, but not fractions, decimals, or irrational numbers.

Which of the given number sets contains all integer numbers?

This problem asks which set of given numbers contains all integers. Learn how to identify integer numbers from a set that includes square roots, fractions, and decimals, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation