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Question
Which of the following is a correct statement?
Options
Sum of two irrational numbers is always irrational
Sum of a rational and irrational number is always an irrational number
Square of an irrational number is always a rational number
Sum of two rational numbers can never be an integer
Solution
The sum of irrational number and rational number is always irrational number.
Let a be a rational number and b be an irrational number.
Then,
`(a + b)^2 = a^2 +b^2 + 2ab`
`= (a^2 + B^2) +2ab`
As 2ab is irrational therefore `(a + b)^2` is irrational.
Hence (a + b) is irrational.
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