Question:
Which one of the following statements is true?
(a) The sum of two irrational numbers is always an irrational number
(b) The sum of two irrational numbers is always a rational number
(c) The sum of two irrational numbers may be a rational number or an irrational number
(d) The sum of two irrational numbers is always an integer
Solution:
Since, $-\sqrt{2}$ and $\sqrt{2}-1$ are two irrational number and $-\sqrt{2}+(\sqrt{2}+1)=1$
Therefore, sum of two irrational numbers may be rational
Now, let $\sqrt{3}$ and $\sqrt{2}-\sqrt{3}$ be two irrational numbers and $\sqrt{3}+(\sqrt{2}-\sqrt{3})=\sqrt{2}$
Therefore, sum of two irrational number may be irrational
Hence the correct option is 
.