Classify each number as being a natural number (N), whole number (W), integer (I), rational number (Q), and/or irrational number (Q′).

ⓐ  36−−√
 
ⓑ  83

Let's classify each number according to the following categories:

- **Natural Numbers (N):** These are positive counting numbers: 1, 2, 3, etc.
- **Whole Numbers (W):** These include all natural numbers and zero: 0, 1, 2, 3, etc.
- **Integers (I):** These include all whole numbers and their negatives: ..., -2, -1, 0, 1, 2, etc.
- **Rational Numbers (Q):** These are numbers that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \).
- **Irrational Numbers (Q′):** These are numbers that cannot be expressed as a fraction of two integers (e.g., \( \pi \), \( \sqrt{2} \)).

Now, let's classify the numbers:

### ⓐ \( \sqrt{36} \)

- \( \sqrt{36} = 6 \)
- **Natural Number (N):** Yes, 6 is a natural number.
- **Whole Number (W):** Yes, 6 is a whole number.
- **Integer (I):** Yes, 6 is an integer.
- **Rational Number (Q):** Yes, 6 can be expressed as \( \frac{6}{1} \), so it's rational.
- **Irrational Number (Q′):** No, \( \sqrt{36} \) is not irrational because it simplifies to a rational number (6).

So, \( \sqrt{36} \) is a **natural number, whole number, integer, and rational number**.

### ⓑ 83

- 83 is a positive integer.
- **Natural Number (N):** Yes, 83 is a natural number.
- **Whole Number (W):** Yes, 83 is a whole number.
- **Integer (I):** Yes, 83 is an integer.
- **Rational Number (Q):** Yes, 83 can be expressed as \( \frac{83}{1} \), so it's rational.
- **Irrational Number (Q′):** No, 83 is not irrational.

So, 83 is a **natural number, whole number, integer, and rational number**.

### Summary:
- **ⓐ \( \sqrt{36} \):** N, W, I, Q
- **ⓑ 83:** N, W, I, Q

Would you like more details or have any questions?

Here are 5 related questions:
1. Can an irrational number also be a rational number?
2. Is \( \pi \) a rational or irrational number?
3. How do you determine if a square root is rational or irrational?
4. Is zero considered a natural number or just a whole number?
5. What is the smallest positive integer?

**Tip:** A square root of a perfect square is always a rational number.

Classify each number as being a natural number (N), whole number (W), integer (I), rational number (Q), and/or irrational number (Q′). ⓐ  √36  ⓑ  83

Discover how to classify numbers like √36 and 83 as natural, whole, integers, rational, or irrational. Learn the rules for classifying numbers and the difference between rational and irrational numbers. Suitable for students in Grades 6-8.

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