Answers:

(i) Consider,

5 + 3√2 be rational.

5 and 5 + 3√2 are rational.

∴ (5 + 3√2 – 5) = 3√2 = rational

∴ 1/3 × 3√2 = √2 = rational

This contradicts the fact that √2 is irrational.

The contradiction arises by assuming 5 + 3√2 is rational.

5 + 3√2 is irrational.

(ii) Consider,

3√7 be rational.

1/3 × 3√7 = √7 = rational

This contradicts the fact that √7 is irrational.

The contradiction arises by assuming 3√7 is rational.

Thus, 3√7 is irrational.