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 an irrational number
(D) Sum of two rational numbers can never be an integer

Explanation

`Sum of a rational and irrational numbers is always an irrational number` is correct statement.
Verification of each statements:
Statement A: Sum of two irrational numbers is always irrational.
Example: ``sqrt 2+(− sqrt 2) = 0, sqrt 3+ sqrt 3 =2√3`
From the above two examples we can say that sum of two irrationals is not always an irrational. So the given statement is false.
Statement B: Sum of a rational and irrational number is always an irrational number.
Example: `2 + sqrt 3 is 3.732142857...` which is an irrational number. So the statement is true.
Statement C: Square of an irrational number is always a rational number.
Example: `(sqrt 3)^(1/3) = (sqrt 9)^(1/3)` which is an irrational. So, the given statement is false.
Statement D: Sum of two rational numbers can never be an integer.
Example: `2 + 4 = 6`, which is an integer. So, the given statement is false.