Let, 5 + 3√2 be rational.
Hence, 5 and 5 + 3√2 are rational.
∴ (5 + 3√2 – 5) = 3√2 = rational [∵Difference of two rational is rational]
∴ 1 3 × 3√2 = √2 = rational [∵Product of two rational is rational]
This contradicts the fact that √2 is irrational.
The contradiction arises by assuming 5 + 3√2 is rational.
Hence, 5 + 3√2 is irrational.