Question

prove that 6+ root 2 is an irrational number
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Answer 1

Answer:

because when it is added to rational it gives rational

Answer 2

Answer:

let us assume, to the contrary, that 6+root 2 is rational

That is, we can find coprime a and b (b is not equal to 0) such that 6+root 2 = a/b

therefore, 6+a/b= root 2

rearranging this equation, we get root 2=6+a/b

=6b+a upon b

since a and b are integers, we get 6+a/b is rational, and so root 2 is rational

but this contradicts the fact that root 2 is irrational

This contradiction has arisen because of our incorrect assumption that 6+ root 2 is rational

so, we conclud that 6+root 2 is irrational.