Question 1033666
Suppose {{{1-1/sqrt(2)}}} is a rational number. Then it can be expressed as the ratio of two positive, relatively prime whole numbers a and b such that {{{1-1/sqrt(2)= a/b}}}.  (It is safe to assume that b > a.)


But if this were the case, then {{{sqrt(2) = b/(b-a)}}}, a ratio of two whole numbers.  Contradiction.  

Hence {{{1-1/sqrt(2)}}} must also be irrational.