Prove by contradiction that 6 \sqrt{6}\,6 is irrational, beginning by assuming that 6 \sqrt{6}\,6 can be expressed in the form ab\displaystyle \frac{a}{b}ba where a a\,a and b b\,b are integers with no common factor (except 1)
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.