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Question

Prove that (35) is an irrational number

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Solution

Let us assume that 35 is a rational number
Then. there exist coprime integers p, q,q0 such that
35=pq
=>5=3pq
Here, 3pq is a rational number, but 5 is a irrational number.
But, a irrational cannot be equal to a rational number.This is a contradiction.
Thus, our assumption is wrong.
Therefore 35 is a irrational number.

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