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.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.