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.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.