Which of the following is a correct statement?

MCQ

Which of the following is a correct statement$?$

A
Sum of two irrational numbers is always irrational.
✓
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.

✓

Answer

Correct option: B.

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

$a$.Is incorrect, because sum of two irrational numbers is not an irrational number always.
It can also be a rational number
i.e. if we add $2+\sqrt{3}$ and $2-\sqrt{3},$ sum comes out to be $2+\sqrt{\not\text{3}}+2-\sqrt{\not\text{3}}=4,$ which is a rational number.
$b$.Is correct, if a rational number is added to an irrational number means to a Non$-$ terminating$-$repeating number, the sum will also be non$-$terminating and Non$-$repeating number,
i.e an irrational number.
Example: a rational number $'2\ '$ and an irrational no $'\sqrt{3}\ '$ is added, sum $=2+\sqrt{3}$ which is again a non$-$terminating and non$-$repeating number, hence an irrational number always.
$c$.Is incorrect, Square of an irrational number is not necessarily a rational number.
Again it can be either a rational or irrational.
i.e $(\sqrt{2})^2=2 ($Rational$)$
$(2+\sqrt{3})^2=4+3+2\times2\sqrt{3}=7+4\sqrt{3}($ irrational$)$
$d$.Is incorrect, Sum of two rational numbers can be an integer and a rational number both.
i.e $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}($ Rational number$)$
Hence, correct option is $(b).$