From the following list of numbers: $$ -2 ; \frac{1}{4} ; \sqrt{3} ; \sqrt{16} ; 0 ; 4 ; \sqrt{-5} $$, write down all the $$ \begin{array}{llll} ext { (1) natural numbers } & ext { (2) whole numbers } & ext { (3) integers } \ ext { (4) rational numbers } & ext { (5) irrational numbers } & ext { (6) real numbers }\end{array} $$

Question

From the following list of numbers: $$ -2 ; \frac{1}{4} ; \sqrt{3} ; \sqrt{16} ; 0 ; 4 ; \sqrt{-5} $$, write down all the $$ \begin{array}{llll}	ext { (1) natural numbers } & 	ext { (2) whole numbers } & 	ext { (3) integers } \ 	ext { (4) rational numbers } & 	ext { (5) irrational numbers } & 	ext { (6) real numbers }\end{array} $$

UpStudy AI · Accepted Answer

Let's classify each number from the list $$ -2 ; \frac{1}{4} ; \sqrt{3} ; \sqrt{16} ; 0 ; 4 ; \sqrt{-5} $$ into the specified categories:

### 1. Natural Numbers
**Definition:** Positive integers (1, 2, 3, ...)

- **4** (since $$ \sqrt{16} = 4 $$ and 4 is a positive integer)

**Natural Numbers:**  
$$ 4 $$

---

### 2. Whole Numbers
**Definition:** Natural numbers including zero (0, 1, 2, 3, ...)

- **0**
- **4**

**Whole Numbers:**  
$$ 0, \, 4 $$

---

### 3. Integers
**Definition:** Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...)

- **-2**
- **0**
- **4**

**Integers:**  
$$ -2, \, 0, \, 4 $$

---

### 4. Rational Numbers
**Definition:** Numbers that can be expressed as a fraction $$\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b \neq 0$$

- **-2** ($$-2 = \frac{-2}{1}$$)
- **$$\frac{1}{4}$$**
- **0** ($$0 = \frac{0}{1}$$)
- **4** ($$4 = \frac{4}{1}$$)

**Rational Numbers:**  
$$ -2, \, \frac{1}{4}, \, 0, \, 4 $$

---

### 5. Irrational Numbers
**Definition:** Real numbers that cannot be expressed as a simple fraction; their decimal expansions are non-repeating and non-terminating

- **$$\sqrt{3}$$**

**Irrational Numbers:**  
$$ \sqrt{3} $$

---

### 6. Real Numbers
**Definition:** All rational and irrational numbers; excludes imaginary numbers like $$\sqrt{-5}$$

- **-2**
- **$$\frac{1}{4}$$**
- **$$\sqrt{3}$$**
- **$$\sqrt{16}$$** (which is 4)
- **0**
- **4**

**Real Numbers:**  
$$ -2, \, \frac{1}{4}, \, \sqrt{3}, \, 4, \, 0 $$

---

### Summary

1. **Natural Numbers:**  
   $$ 4 $$

2. **Whole Numbers:**  
   $$ 0, \, 4 $$

3. **Integers:**  
   $$ -2, \, 0, \, 4 $$

4. **Rational Numbers:**  
   $$ -2, \, \frac{1}{4}, \, 0, \, 4 $$

5. **Irrational Numbers:**  
   $$ \sqrt{3} $$

6. **Real Numbers:**  
   $$ -2, \, \frac{1}{4}, \, \sqrt{3}, \, 4, \, 0 $$

Note that **$$\sqrt{-5}$$** is **not** a real number; it is an imaginary number and does not fit into any of the above real number categories.
- **Natural Numbers:** 4 - **Whole Numbers:** 0, 4 - **Integers:** -2, 0, 4 - **Rational Numbers:** -2, 1/4, 0, 4 - **Irrational Numbers:** √3 - **Real Numbers:** -2, 1/4, √3, 4, 0

From the following list of numbers: , write down all the

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