Choose which set or sets the following number belongs to.  Be sure to account for ALL sets.

negative StartRoot 8 EndRoot−8

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Part 1

Select all that apply.

A.

natural numbers

B.

integers

C.

irrational numbers

D.

whole numbers

E.

rational numbers

The expression given is \(-\sqrt{8}\). Let's determine which sets this number belongs to:

1. **A. Natural numbers**: Natural numbers are positive integers (1, 2, 3, ...). Since \(-\sqrt{8}\) is not a positive integer, it is not a natural number.

2. **B. Integers**: Integers include all whole numbers, both positive and negative, as well as zero (..., -2, -1, 0, 1, 2, ...). \(-\sqrt{8}\) is not an integer because it is not a whole number; it's a non-integer negative number.

3. **C. Irrational numbers**: Irrational numbers cannot be expressed as a fraction of two integers. The square root of 8 (\(\sqrt{8}\)) is not a perfect square and cannot be expressed as a fraction. Therefore, \(-\sqrt{8}\) is irrational.

4. **D. Whole numbers**: Whole numbers are non-negative integers (0, 1, 2, 3, ...). \(-\sqrt{8}\) is negative and not a whole number.

5. **E. Rational numbers**: Rational numbers are numbers that can be expressed as a fraction of two integers. \(-\sqrt{8}\) cannot be expressed as such a fraction because \(\sqrt{8}\) is irrational. Therefore, \(-\sqrt{8}\) is not a rational number.

Thus, \(-\sqrt{8}\) belongs to the set **C. Irrational numbers**.

Would you like more details on these classifications or have any other questions?

### Related Questions:
1. Why is \(-\sqrt{8}\) classified as an irrational number?
2. Can irrational numbers ever be integers?
3. What is the difference between rational and irrational numbers?
4. How would you classify \(\sqrt{9}\)?
5. Is \(\sqrt{8}\) a real number? Why or why not?
6. Are all square roots irrational numbers?
7. Can an irrational number be negative?
8. How do you simplify square roots like \(\sqrt{8}\)?

**Tip:** Remember that an irrational number is any number that cannot be written as a simple fraction, which often includes square roots of non-perfect squares.

Understand which sets the number -√8 belongs to: natural numbers, integers, irrational numbers, whole numbers, or rational numbers. Learn why -√8 is classified as an irrational number and explore related concepts. Suitable for students in Grades 7-9.

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