Classify . 3(p)/4;-1/2;radical 5 ; -(radical)36; 57 , 3 periodic ; e

Let's classify the given numbers based on their mathematical categories:

1. **\( \frac{3p}{4} \)** – Assuming \( p \) represents a rational number, this is a **rational number** since it's in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \).

2. **\( -\frac{1}{2} \)** – This is a **rational number** because it can be expressed as a fraction of two integers, \( \frac{-1}{2} \).

3. **\( \sqrt{5} \)** – This is an **irrational number** because \( \sqrt{5} \) is not a perfect square, and its decimal form is non-repeating and non-terminating.

4. **\( -\sqrt{36} \)** – Since \( \sqrt{36} = 6 \), this simplifies to \( -6 \), which is an **integer** (and also a rational number, as it can be written as \( \frac{-6}{1} \)).

5. **57** – This is an **integer** and also a **rational number** because any integer can be written as a fraction (e.g., \( \frac{57}{1} \)).

6. **3 periodic** – This refers to the **rational number** 3.333... (repeating), which can be written as \( \frac{10}{3} \), making it a rational number.

7. **\( e \)** – The number \( e \) (Euler's number) is an **irrational number** because its decimal representation is non-repeating and non-terminating.

### Classification Summary:
- **Rational numbers**: \( \frac{3p}{4}, -\frac{1}{2}, -6, 57, 3 \text{ periodic} \)
- **Irrational numbers**: \( \sqrt{5}, e \)
- **Integers**: \( -6, 57 \)

Would you like more details or have any questions?

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### Related Questions:
1. What is the difference between rational and irrational numbers?
2. How can you prove that \( \sqrt{5} \) is irrational?
3. What is the significance of Euler's number \( e \)?
4. Can you represent periodic decimals as fractions?
5. Why are integers considered rational numbers?

### Tip:
An integer is always a rational number because it can be expressed as a fraction with 1 as the denominator.

Classify numbers like 3(p)/4, -1/2, √5, -√36, 57, 3 periodic, and Euler's number e into rational, irrational, and integer categories. Understand the mathematical concepts behind these classifications and apply key theorems related to number types. Suitable for Grades 9-12.

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