Question

6 + root 2 prove that the following are it
Irrational

Answer 1

Answer:

let us assume on the contrary that 6+√2 is rational. Then there exist Co-Prime positive integers a&b such that

6+ √2=a/b

=>√2= a/b - 6

=>√2 = (a-6b)/b

=> √2 is rational [as a,b are integers, so ( a-6b)/bis a rational]

This contradicts the fact that root 2 is irrational... So, our assumption is wrong. Hence 6+ root 2 is an irrational number.......