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.