Question

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Answer 1

(i) Let the two irrational numbers as `2 + sqrt(3)` and `3  – sqrt(3)`

Their sum is `2 + sqrt(3) + 3 - 3sqrt(3)` which is a rational number.

But the sum of `3 + sqrt(5)` and `4 - sqrt(7)` is not a rational number.

So the sum of two irrational numbers is either rational or irrational.

(ii) Again taking two irrational numbers as π and `3/pi` their product is `sqrt(3)` and `sqrt(2)`

= `sqrt(3) xx sqrt(2)` which is irrational

So the product of two irrational numbers is either rational or irrational.