An irrational number happens to be one that cannot be expressed in the form of a ratio. Considering another angle a real number that is not a rational number is an **irrational number**. The discovery of irrational number took place in the 5^{th} century. The sad part was this theory did not have a lot of takers and was dumped. But irrational numbers exist, and if you have an idea about the concept of it things become easy.

## The properties of an irrational number

The properties of an irrational number makes it easy for us to understand as you can choose them from a set of real numbers. Let us get to some of the properties of an irrational number

- They consist of non- terminating and non- recurring decimals
- They are an extension of real numbers
- The moment you go on to add a rational and an irrational number together, the sum that emerges is an irrational number only. Coming to an irrational number y and a
**rational number**x the result X+ Y= an irrational number - The addition, multiplication, division or subtraction of a couple of irrational numbers will not always be a rational number
- When it comes to a couple of irrational numbers, you multiply it by a non- zero rational number, the product would be turning out to be an irrational number.

## The process to identify an irrational number

It is an obvious fact that an irrational number turns out to be a real number. It cannot be expressed in the form of p/q and q does not equal to zero. Conversely if any number can be expressed in the form of p/ q and q does not equal to zero it is a classic example of a rational number.

## The symbol of irrational numbers

Before knowing the symbols of irrational numbers let us try to understand the symbols of other numbers

- N is for natural numbers
- I for imaginary number
- R for rational number
- Q for rational number

The real numbers is a combination of both rational and irrational numbers.( R-Q) indicates that it is possible to arrive at an irrational number where you deduct rational number from the real number.

## Interesting points of rational and irrational numbers

A proper analysis of rational numbers and irrational numbers gives you a proper understanding on why it is part of the real numbers.

- The product of a couple of irrational numbers may turn out to be rational or irrational.
- Coming to the set of an irrational number it would not be closed under the process of multiplication that would be the set of rational number
- The multiplication or addition of a couple of irrational numbers may turn out to be rational.
- It has to be said that rational along with irrational number is not the same. It is necessary that all the numbers have to be represented in the form of p/q which are integers. Here q will not be equal to 0 that would not be a rational number. Another important point to consider is that it is not possible to express irrational number in the form of p/q
- The major difference between rational and irrational numbers is that it would not be terminating and non -repeating. On the other hand an irrational number would repeat and neither terminate after a specific set of decimal points

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