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 Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 261 questions covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof, matched to the Edexcel A Level Maths (9MA0) 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.
