Show that 11 - V2 is an irrational, if given that v2 is an irrational. – InterviewSolution

1.

Show that 11 - V2 is an irrational, if given that v2 is an irrational.

Answer»

We know √2 is irrational.

Let 11 - √2 be rational then

11 - √2 = r , where r is rational

11 - r = √2

This is an absurd result as LHS is rational and RHS is irrational .

So, a contradiction to our assumption hence 11 - √2 is irrational

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