Question

If x and y are irrational numbers, show that it does not follow that x + y and xy are irrational

Answer 1

Given : x and y are irrational numbers

To Show :  x & y does not  follow that x + y and xy are irrational

Solution:

Let say

x  = 2  +  √3

y = 2  - √3

x + y

= 2 + √3 + 2 - √3

= 4

4 is not irrational

hence x + y is not irrational

xy

=  (2 + √3) (2 - √3)

= 4 - 3

= 1

1 is not irrational

hence xy is not irrational

Hence we Shown above That   x + y and xy does not follow that they are irrational if x & y are irrational numbers

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