A sculpture is designed in the shape of a perfect cube. The artist specifies that the volume of the sculpture must be exactly 7 m37\text{ m}^37 m3. An architect claims that the side length of this cube, LLL, can be expressed as a rational number (a fraction of two integers in its simplest form).
Prove by contradiction that the architect's claim is false.
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.