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Which of the following is a correct statement? 

A. Sum of two irrational numbers is always irrational. 

B. Sum of a rational and irrational number is always an irrational number 

C. Square of an irrational number is always a rational number 

D. Sum of two rational numbers can never be an integer

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Let the rational number be of the form \(\frac{p}q\) , where p ∈ Z, while the rational number be r. If r + \(\frac{p}q\) is a rational then we have that,

\(r+\frac{p}q\) = \(\frac{a}b\) for some ∈ a Z and b ∈ Z \ {0}. This means that r = \(\frac{a}b - \frac{p}q\) \(\frac{aq-bp}{bq}\) where aq – bp ∈ Z and Hence, it is an irrational number

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