i. Give an example of two irrationals whose sum is rational.
ii. Give an example of two irrational whose product is rational.
Let’s take (2 + 
) and (2 ‒ 
).
These are irrational numbers.
Their sum = (2 + 
) + (2 ‒ 
) = 4 {which is rational}.
ii) Let’s take (3 + 
) and (3 ‒ 
).
These are irrational numbers.
Their product = (3 + 
) × (3 ‒ 
) = 9 + 3√2 – 3√2 – (√2)2
= 9 – 4 = 5 {which is rational}
5