Q. 14.3( 21 Votes )

Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.

Answer :

Given: x is rational number and y is irrational number.

Yes, x + y is necessarily an irrational number.


Example: Let x = 2, which is rational.


Let y = √2, which is irrational.


Then, x + y = 2 + √2, which is irrational.


Sum of a rational and an irrational number is always irrational.


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