Assume that 2=a/b\sqrt{2}=a/b2=a/b, where a a\,a and b b\,b are integers with no common factors. Show that a a\,a and b b\,b are both even.
Hence prove by contradiction that 2 \sqrt{2}\,2 is irrational
366 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.