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Question
Which one of the following statements is true?
Options
The sum of two irrational numbers is always an irrational number
The sum of two irrational numbers is always a rational number
The sum of two irrational numbers may be a rational number or an irrational number
The sum of two irrational numbers is always an integer
Solution
Since, `-sqrt2 and sqrt2 - 1` are two irrational number and `-sqrt2+(sqrt2+1 = 1`
Therefore, sum of two irrational numbers may be rational Now, let `sqrt3 and sqrt2 - sqrt3 `be two irrational numbers and`sqrt3 +(sqrt2 - sqrt3) = sqrt2`
Therefore, sum of two irrational number may be irrational.
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