Question

prove that 5√2 is irrational? ​

Answer 1

Answer:

Step-by-step explanation:We have to prove  

2

​  

 is irrational.

Let us assume  

2

​  

 is rational  

2

​  

=  

b

a

​  

     ( a and b has no common factions but 1 )

⇒2=  

b  

2

 

a  

2

 

​  

 

    2b  

2

=a  

2

   ( hence a is even )

let a=2k

⇒2b  

2

=(2k)  

2

 

⇒b  

2

=2k  

2

   ( Hence b is even as well )

This contradicts as both a and b are even,  ( 2 as common factor )

Hence,  

2

​  

 is irrational.

Hence, proved.