# Irrational Number Definition

It is one of the two major types of real numbers. The set of **irrational numbers** includes all those numbers that **can’t be written in the form of a fraction**. It means a number that has no **defined denominator** will be termed an irrational number.

**Note:**

Read about Real Numbers here.

**Table of Contents**

For example, √2 ,√5 ,√7,√3 are included in a set of irrational numbers. There are many other numbers that are irrational when we solve them. **“Pi”**, a famous constant in Mathematics, is also an **irrational number**.

### Fun Facts about Irrational Number

- The
**Sum**of an**irrational**number with a**rational**number will always be an**irrational number**. - The product of a
**rational**number with an**irrational**number will be an irrational number. - The
**multiplication**of two**irrational**numbers gives a**rational**number as the output.

### How to check if a number is irrational or not?

For a Mathematics student, it is important to learn how he can check if a number is irrational or not. Many students try to find this by **dividing** which takes a lot of time and effort. The simplest approach to check this is by evaluating the **decimal part** of the solution.

If the decimal part of the solution is neither **recurring** nor **terminating**, it means that the given number is **irrational**. But if the decimal part has been terminated after some digits, it shows that the number is not **irrational**.

### Common sets included in irrational numbers

An irrational number is a type of real number that can’t be defined in terms of ratio or fraction. It includes multiple sets of numbers that we are going to mention here.

- Natural numbers
- Whole numbers
- Integers

**Note:**

Read about **Natural Numbers**, **Whole Numbers**, and Integers here.

### What is the difference between Rational and Irrational Numbers?

The main difference between Rational and Irrational numbers is their appearance. If a number can be written in the form of a fraction, it will be termed a **Rational** number otherwise the number will be **irrational**.

**Note:**

Read about Rational Numbers here.

### FAQ's

**Is Pi an irrational number?**

Yes, Pi is an irrational number because its decimal part is neither recurring nor terminating.

**What is the opposite of an irrational number?**

The opposite of an irrational number is a rational number. Both sets are two major types of real numbers.

**Is 2/3 a rational number or an irrational number?**

2/3 is a rational number because its decimal part includes repeated terms.

**Are all integers are irrational?**

No, all integers are not irrational. The set of integers includes both rational and irrational numbers.