Prove the following statement: if x is irrational and y is irrational then x+y is irrational

Chardonnay Felix

Chardonnay Felix

Answered question

2021-02-12

Prove the following statement: if x is irrational and y is irrational then x+y is irrational

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2021-02-13Added 100 answers

If x and y are both irrational numbers then x+y need not to be irrational number. As a example, take x=2 and y=1+2,then x+y=2+(1+2)=1,
which is rational. But if xx and yy bothrational, say
x=ab,y=cd,
where a,b,ca,b,c and dd are integers with b,db,d not equal to 0.0. Now
x+y=ab+cd=ad+bcbd.
Therefore, x+y is rational since ad+bc,bd are integers and bd not equal to 0.0.

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