Question

example of two irrational numbers whose sum and product both are rational

Answer 1

Two irrational numbers are under root 1 and under root 1 Sum of two irrational numbers Under root 1 + under root 1=2 Sum of two irrational numbers Under root 1 × under root 1= 1
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Answer 2

 They are sqrt(2) and -sqrt(2)

The sum is zero and product is -2.