Can You Show That The Sum Of An Irrational And A Rational Number Is Always An Irrational Number?

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Anonymous answered
Let r=p1/q 1is a rationale number and s is irrational.
We have to prove that r+s is irrational number.
Suppose r+s is rational
 r+s= p/q
s=p/q-p1/q1= (pq1-p1q)/qp1=p2/q2  
This is contradiction because it is given that s is irrational. So our supposition is wrong.
Hence r+s is irrational.
Anonymous Profile
Anonymous answered
Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational.

1.a +b =c
where a and c are rational and c is irrational.

subtracting the same number a from each side.

3.b is irrational c-a is a rational number we arrived at a contradiction .
So thesum is an irrational number

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