![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Explain the basic mathematical operations on irrational numbers.
Addition of the Irrational Numbers :
Irrational Number $+$ Irrational Number $=$ May or may not be an Irrational Number
Example: $√2 = 1.414… , √3 = 1.732…$
$√2 + √3$
$= 1.414… + 1.732…$
$= 3.146……$
3.146…… is non-repeating and non terminating. Therefore, it is an irrational number.
$( 1 – √2 ) + √2$
$= 1 – √2 + √2 = 1$
1 is a rational number.
The addition of two irrational numbers may or may not be an irrational number.
Subtraction of the Irrational Numbers
Irrational Number $–$ Irrational Number $=$ May or may not be an Irrational Number
$√2 = 1.414… , √3 = 1.732… ,$
$√3 – √2$
$= 1.732… – 1.414… = 0.318…$
0.318… is non-repeating and non terminating. Therefore, 0.318.... is an irrational number.
$( 1 + √2 ) – √2$
$ = 1 + √2 – √2 = 1$
1 is a rational number.
The subtraction of two irrational numbers may or may not be an irrational number.
Multiplication of the Irrational Numbers
Irrational Number $\times$ Irrational Number $=$ May or may not be an Irrational Number
$√2 = 1.414… , √3 = 1.732…$
$√2 \times √3$
$= 1.414… \times 1.732… = 2.449….$
2.449..... is non-repeating and non terminating. Therefore, 2.449..... is an irrational number.
$( 2 √3 ) \times √3$
$= 2 \times √3 \times √3 = 2 \times 3 = 6$
6 is a rational number.
The multiplication of two irrational numbers may or may not be an irrational number.
Division of the Irrational Numbers
$\frac{Irrational Number}{Irrational Number} = May or may not be an Irrational Number$
$√2 = 1.414… , √3 = 1.732… , √5 = 2.236…$
$\frac{\sqrt{2}}{\sqrt{3}}=\frac{1.414..}{1.732..}=0.816..$
When we divide two irrational numbers we may or may not get an irrational number.