Answer to Question #103941 in Abstract Algebra for BIVEK SAH

Question

Prove or disprove that 2 + (11)^1/2∈Q .

Answer 1

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

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

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

Proved.