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.
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.