Which one of the following statements is true?

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 .

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