An architect is designing a modern sculpture consisting of two cubes. The volume of the larger cube is exactly 7 times the volume of the smaller cube. Let L L\,L represent the ratio of the side length of the larger cube to the side length of the smaller cube, such that L=73L = \sqrt[3]{7}L=37.
Prove by contradiction that L L\,L is 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.
