Question #103941
Prove or disprove that 2 + (11)^1/2∈Q .
1
Expert's answer
2020-03-12T12:02:30-0400

11=3.31662479036...\sqrt{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} is irrational.

Thus, 2+112+ \sqrt{11} is also irrational.

    2+11Q\implies 2+\sqrt{11} \notin Q

Proved.


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