Question

Prove that 6+√2 is irrational​

Answer 1

Answer:

Step-by-step explanation:

Let us assume 6+  2  is rational. Then it can be expressed in the form  

q  p , where p and q are co-prime

Then,                                                                                                                           6+  2 =  q  p

​  

2  =  q  p −6

2 =  q  p−6q

​  

 -----(p,q,−6 are integers) q

p−6q  is rational

But,   2  is irrational.

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

Hence, 6+  2 is irrational