# What Are The Examples Of Irrational Numbers?

Look back at the old days, when your teacher used to teach examples of irrational numbers. And everyone was with a common doubt, is 0 an irrational number? Well, to get its answer, stay connected with us till the end of this article. After reading this article, you won’t need to check for every number, because in this article we will give you a basic idea about irrational numbers. After getting this idea, you will tell whether it is an irrational number or a rational number within a fraction of time. Below, we will give you the definition of rational and irrational numbers with examples also. Let’s get started without delay and know the examples of irrational numbers.

**What Are The Irrational Numbers? **

Before moving ahead, it is very crucial to know what the irrational number actually is. When you understand the basic idea behind irrational numbers then you will easily identify the irrational number. Well, irrational numbers are those numbers that can not be represented as simple fractions. They can not be expressed as a ratio, such as a/b, where a and b are integers, b≠0. In simple words, irrational numbers are the contradiction of rational numbers. But, what is the rational number? Well, rational numbers are those numbers that can be expressed as the ratio of two integers, where the denominator shouldn’t be equal to zero.

An irrational number symbol is R/Q, where the backward slash symbol denotes ‘set minus’. It can also be denoted as R-Q, which refers to the difference between a set of real numbers and a set of rational numbers.

Now, you have an idea of irrational numbers. Let’s have a look at the list of irrational numbers examples.

**What Are The Examples Of Irrational Numbers? **

Here are some examples of irrational numbers,

- Pi
- √21
- √17
- √2
- √3
- √19

Let’s explain what are examples of irrational numbers.

**10 Examples Of Irrational Numbers **

There are many examples of irrational numbers in decimal form, here we have selected some real-life examples of irrational numbers. Let’s have a look.

**1. Pi **

There are multiple examples of rational numbers and irrational numbers, one of the very famous examples of irrational numbers in fraction form is Pi. When you get the actual value of Pi, it will be 3.14285714285…. Here you can see the number which is non-terminating and is repeating. Hence, it is obeying the property of the irrational number, and therefore, Pi is an irrational number. We use another substitute value for Pi while solving numerical, and that is 22/7. Now, here 22/7 is not irrational but a rational number. Similarly, 0 is also not an irrational number, but a rational number.

**2. √21 **

One of the other examples of irrational numbers is under root 21. When you take its root, then you will get the value of 4.12310562562…, which is a non-terminating value, and hence under root 21 is also an irrational number. But if this 21 is outside the root, then it would be a rational number.

**3. √17**

One of the examples of irrational numbers in real life is the under root 17. The examples of irrational numbers and rational numbers are interlinked. Why? Because, when you take this 17 out of the root, then it will be a rational number, and under a root, it is an irrational number. The value√17 is 4.12310562562…, which is a non-terminating value again. And hence this is an irrational number.

**4. √2 **

One of the examples of irrational numbers in daily life among the examples of rational and irrational numbers is under root 2.√2 which is considered an irrational number. Because, according to some basic properties of an irrational number, any number that has a non-terminating and non-repeating decimal expansion is always an irrational number.

**5. √3 **

Like, √2 under root 3 is also an irrational number. Because the actual values of this term when you take its root then it will be 1.73205080757… This will continue and never end, therefore it is also considered an irrational number.

**6. √19 **

The value √19 is 4.3588989435…, which is a non-terminating value, and hence this is an irrational number. This number can be a rational number when you remove the sign of root from it. So, you can say, an irrational number is formed from the combination of rational numbers. You can also say that an irrational number is not completely divisible by any number.

Till now, you have learned more than five examples of irrational and rational numbers.

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**FAQ**

**Is 7 A Irrational Number?**

Therefore, the given number 7 is a rational number. Note: Based on the above solution, we can make a conclusion that all natural numbers are rational numbers as they all can be expressed as a fraction.

**Is 4 A Irrational Number?**

Yes, 4 is a rational number because it satisfies the condition of rational numbers. 4 can be expressed as a ratio such as 4/1, where the denominator is not equal to zero.

**Is 8 An Irrational Number?**

The number 8 is a rational number because it can be written as the fraction 8/1.

**Is Root 81 Irrational?**

The square root of 81 is a rational number as it can be expressed in the form of p/q.

**How Can You Tell If A Number Is Irrational?**

Irrational numbers **have endless non-repeating digits after the decimal point**. Below is an example of an irrational number: Example: √8 = 2.828…

**Conclusion **

By reading this article, you have understood the definition of irrational numbers with examples in detail. After understanding the above-mentioned examples of irrational numbers, you may be thinking about how to write these non-terminating values while solving numerical ones. Well, while actually using these types of values, you don’t need to write them fully, so you can write them as round figures or approximations. For example, if there is a value 1.234543…, which is non-terminating, then you can write it as 1.235 only. Now, you know all the examples of irrational numbers.