Introduction To Irrational Number

To  Understand what  is  an  Irrational number we have to understand what is a rational  number? Rational number are those numbers which can be expressed in the form of numerator / denominator. Every rational numbers can be expressed as decimal form or in non- terminating  repeating decimal form..

Definition of Irrational number: Irrational numbers are those numbers which cannot be expressed  in  the form of numerator / denominator. all non- terminating non- recurring decimals are irrational number.

What is a irrational number
According to definition of Irrational numbers : Any number that cannot be expressed in the form of p/q , where p , q are integers , q>0 , p and q have no common factor (except 1) is called an irrational number.

What are irrational number

• Negative of an  irrational number  is an irrational  number. 
• The sum of a rational number and an irrational number is considered as an irrational number.
• The product of a non-zero rational number and an irrational number is found to be irrational in nature.
• The sum, difference , product , and quotient of two irrational numbers need not to be an  irrational number  because the sum of the irrational numbers √3  and  -√3 is 0 which is a rational number, whereas the sum of irrational number √2 and √5 is an irrational number
• The difference of an irrational numbers √2 and  -√2 is zero which is a rational number but √5 and √ 6 difference is irrational  number.
• The product of √18 and √ 2 is 6, which is a rational number and √7 and √6 is √42 which is irrational.
• The quotient  of irrational number √12 and √ 3 is 2 , which is a rational number  and √12 and √4 is √3 is irrational number.

What is an irrational number

A  number is an irrational number  , if it has non-terminating  an non repeating decimal representation.

• Let  us  take some Irrational numbers examples 0.12112111211112………., 0.30003000030000003…………….. cannot be expressed  in the form of p/q. 
• The decimal representation of √2=1.414215…………………. is neither terminating nor repeating so , it is an irrational number.