Question

show that 4√2is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

Assume that,

4  

2

​  

 is a rational number.  

Then, there exists coprime positive integers p & q such that  

4  

2

​  

=  

q

p

​  

 

2

​  

=  

4q

p

​  

 (∵ p & q are integers)

⇒  

4q

p

​  

 is rational

⇒  

2

​  

 is rational

This contradict the fact that  

root2 is irrational. so our assumption is incorrect.

Hence 4-  root2 is irritational.