21. Exemplar Example Problems I

1. Are there two irrational numbers whose sum and product both are rationals? Justify.

 

noyes there are two irrational numbers whose sum and product both are rationals

 

2. State whether the following statement is true: There is a number \(x\) such that \(x^2\) is irrational but \(x^4\) is rational. Justify your answer by an example.

 

The given statement is falsetrue