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.