Question

let x and y be rational and irrational number respectively is x+y necessarily an irrational number give an example in support of your answer​

Answer 1

Answer:

Let us assume that x (which is a rational number) = 8

And y (which is an irrational number) = 5.12

On adding x and y  

x + y = 8 + 5.12 = 13.12 which is irrational.

Here, we take another example

Consider x = 15 and y = 5.79

Then the value of x and y will be

x + y =15+5.79 = 20.79

These two examples clearly explains that the addition of a rational and an irrational number leads to an irrational number.

Hence, x + y is an irrational number.