SPS SPS SM 2022 January — Question 7 7 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2022
SessionJanuary
Marks7
TopicProof
TypeContradiction proof of irrationality
DifficultyStandard +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.
Spec1.01d Proof by contradiction

7. Prove by contradiction that \(\sqrt [ 3 ] { 2 }\) is an irrational number.
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7. Prove by contradiction that $\sqrt [ 3 ] { 2 }$ is an irrational number.\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM 2022 Q7 [7]}}