A theoretical chemist determines that a specific bond length LLL is an irrational number. In a molecular model, they define an effective length EEE by scaling LLL by a known non-zero rational factor κ\kappaκ, such that E=κLE = \kappa LE=κL.
Prove by contradiction that the effective length EEE must be an irrational number.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
