Surds – GCSE Maths Revision and Worksheets

Surds is a topic that many students struggle with and therefore require plenty of practise to overcome the challenges that surd questions present. From rationalising surds to simplifying them, there are plenty of different question types that need understanding. On this page you will be able to revise surds for the new GCSE Maths 9-1 course and therefore you will find the new types of questions that have appeared on the most recent papers and specimen papers of Edexcel, AQA and OCR as well as the other major exam boards.

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What you need to know

What you need to know:

Surds are defined to be numbers that we leave in root form, \sqrt{2}, rather than decimal form, 1.414213…, so to express their exact value. You may be asked to simplify surds by various applications of the rule \sqrt{ab} = \sqrt{a}\sqrt{b}; this rule is very important for all the work we do surrounding surds, so familiarity with it is necessary.

We say that a number is in surd form when it cannot be simplified any further. For example, \sqrt{3} is in surd form, however \sqrt{27} can be simplified using the above rule as follows:

\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}

Exam questions often ask that you leave your answers in surd form. In this example, you would likely be deducted a mark if you said that the final answer was \sqrt{27} rather than 3\sqrt{3}.

You are also required to know how to rationalise the denominator of a fraction involving surds. This involves manipulating the fraction so that the bottom of it no longer contains any surds – only whole numbers. You should be able to do this with fractions where the denominator is itself a surd (multiply top and bottom by that surd) as well as with fractions where the denominator is an expression of the form a + \sqrt{b} (multiply top and bottom by a - \sqrt{b}). More than anything else this requires care, so take your time with the arithmetic, especially at the beginning.

Surds is one of those GCSE Maths topics that many students struggle with and as a result teachers are constantly looking for new ways to teach it and provide better resources to help students understand it. The surd revision materials on this page can be used to help support your students both in the classroom and at home. You can find tonnes more GCSE Maths resources on our GCSE Math homepage.

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