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A surd is an irrational root left in exact form. This topic simplifies surds, rationalises denominators and manipulates them in exact calculations. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Simplify by pulling out the largest square factor, so root 50 becomes 5 root 2. Add and subtract only like surds. Multiply by combining under one root. To rationalise a denominator, multiply top and bottom by the surd, or by the conjugate when the denominator has two terms.
Before you start
Before starting, revisit square roots and index laws. It is Higher tier material at GCSE and iGCSE. It then feeds into exact answers in trigonometry, Pythagoras and quadratics. Filed under Number.
What you learn
A surd is a root that can’t be simplified to a whole number, like √2 or √5. Surds let you keep answers exact — and manipulating them is a core Higher skill. A surd is an irrational root — its decimal never ends or repeats, like √2 = 1.41421… We leave it as √2 to stay exact. It’s untidy to leave a surd on the bottom of a fraction. The course works through simplifying surds, operations with surds and rationalising the denominator. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Surds as one of the Number topics in our GCSE course library, at Higher tier. You work through 3 concepts and 2 worked examples, testing yourself at 3 points. Related topics students usually take next include Systematic Listing, Upper & Lower Bounds and Approximation. The Number revision engine gives you as many extra questions as you want, tracked on your skill tree.
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