11=3.31662479036...\sqrt{11}= 3.31662479036...11=3.31662479036... , which cannot be represented in the form p/q , as the fraction part is non-terminating non-recurring .
As this cannot be represented in the form of a rational number, 11\sqrt{11}11 is irrational.
Thus, 2+112+ \sqrt{11}2+11 is also irrational.
⟹ 2+11∉Q\implies 2+\sqrt{11} \notin Q⟹2+11∈/Q
Proved.
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