Prove that 6 √ 2 is irrational | Forums

Prove that 6 + √ 2 is irrational
Submitted on 21/1/2024 | Answered by Vandana Rana

Let us assume 6 +√2 is rational.

Then it can be expressed in the form p/q where p and q are co-prime.

Then,


 6 +√2=p/q
 

 √2 =p/q −6
 

 √2 =(p −6q)/q  -( p,q,−6 are integers)
 

 (p −6q) /q  is rational

But, √2 is irrational.

This contradiction is due to our incorrect assumption that 6+√2 is rational.

Hence, 6 +√2 is irrational