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This topic covers the laws of indices — including negative, zero and fractional powers — and manipulating surds by simplifying, rationalising denominators and combining them: the algebraic foundation for the course. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Apply the index laws — add for multiplication, subtract for division, multiply for a power of a power. Simplify surds by extracting the largest square factor, and rationalise a denominator by multiplying by the surd, or by the conjugate when it has two terms.
Before you start
Check index laws and roots first if this feels hard. It belongs to the Pure 1 specification. From here the path runs to algebraic manipulation throughout the course. Filed under Algebra.
What you learn
To clear a surd from the denominator, multiply top and bottom by its conjugate — change the sign between the terms. The course works through compound indices & index equations, surd manipulation & ‘show that’ and problem-solving with indices & surds. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Indices and Surds as one of the Algebra topics in our A-level course library, at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Nearby topics in the same strand are Inequalities, Modulus Function, Partial Fractions, Quadratic Functions & Discriminant and Solving Quadratics. Endless extra practice on this strand is available on the Algebra revision engine, which generates a fresh question each time.
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