Showing posts with label irrational numbers definition. Show all posts
Showing posts with label irrational numbers definition. Show all posts

Thursday, June 14

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.