Irrational Numbers: Everything you need to know

Irrational numbers can be interpreted as sets of real numbers. These numbers cannot be depicted in the form of fractions. In easy words, irrational numbers are the numbers that can not be depicted in the aspect of a/b. The irrational numbers are shown by using the symbol “P”.

Properties of Irrational Numbers

Some of the most crucial properties of irrational numbers are mentioned below;

When any rational number and any irrational number are added jointly, then the result will be an irrational number.
When any irrational number is multiplied by any rational number, then the result will be an irrational number.
However, the condition is that the rational number should not be zero.
When the lcm of any irrational number is taken, then the value does not exist.
When any two of the irrational numbers are multiplied, then the value, as a result, will be any rational number.

How to Know if a Number is an Irrational Number or Not?

This is one of the most significant and also very essential questions in the minds of learners. To recognize any irrational number, here are a few steps:

The very prime thing that is needed to be noticed is to check if the given irrational number can be conveyed in the fractional form or not. That means if the given number can be formed in a/b form or not.
The next thing that one has to check is that if in the form a/b, b should not be equal to zero.

How to Get the Irrational Numbers?

We can know this more evidently by illustrating an example. An example illustrating the following is mentioned below;

Example 1:To get the irrational numbers that come between the numbers 3 and 5.
Solution:
First of all, we have to look at the numbers and think of the numbers they are the roots of.
√9 is for 3 and √25 is for 5.
Since we have to get the irrational numbers, between the 3 and 5,
We will find the irrational numbers that come between √9 and √25.
Hence, the numbers are
√10, √11, √12, √13, √14, √15, √16, √17, √18, √19, √20, √21, √22, √23, and √24

Examples Of Irrational Numbers

Now, we will be mentioning a few examples of irrational numbers. Those numbers are mentioned below;
√5 – This can not be indicated in the fractional form of a/b. Thus, √5 is considered to be an irrational number.
√11 – This can not be indicated in the fractional form of a/b. Thus, √11 is evaluated as an irrational number.
√21 – Thia can not be demonstrated in the fractional form of a/b. Consequently, √21 is evaluated as an irrational number.
π – This is also evaluated as an irrational number.
√2 – This can not be demonstrated in the fractional form and is thus considered to be an irrational number.

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