Standard +0.8 This is a standard proof by contradiction requiring students to assume √[3]{2} = p/q in lowest terms, cube both sides to get 2q³ = p³, then show both p and q must be even (contradicting lowest terms). While it follows a well-known template similar to proving √2 is irrational, the cube root version requires slightly more algebraic manipulation and careful reasoning about divisibility by 2, making it moderately above average difficulty.