Note that if we add a rational number a, what we get is : [tex] a+\sqrt{2} [/tex], which is again irrational.
a=2, a=0, a=1/2 all are such rational values.
Only when we add [tex]-\sqrt{2} [/tex], we see that we get [tex]-\sqrt{2}+\sqrt{2}=0[/tex], which is rational.
Answer: A
