Let r=p

_{1}/q

_{1}is a rationale number and s is irrational.

We have to prove that r+s is irrational number.

Suppose r+s is rational

Then;

r+s= p/q

p

_{1}/q

_{1}+s=p/q

s=p/q-p

_{1}/q

_{1}= (pq

_{1}-p

_{1}q)/qp1=p

_{2}/q

_{2 }

This is contradiction because it is given that s is irrational. So our supposition is wrong.

Hence r+s is irrational.

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