Answers:
(i) Consider,
3 + √2 be rational.
3 and 3 + √2 are rational.
∴ 3 + √2 – 3 = √2 = rational
This contradicts the fact that √2 is irrational.
The contradiction arises by assuming 3 + √2 is rational.
3 + √2 is irrational.
(ii) Consider,
2 + √5 be rational.
2 + √5 and √5 are rational.
∴ (2 + √5 ) – 2 = 2 + √5 – 2 = √5 = rational
This contradicts the fact that √5 is irrational.
The contradiction arises by assuming 2 – √5 is rational.
Thus, 2 – √5 is irrational.