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Surds - GCSE Maths Definition

Reviewed by: Mark Curtis

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What are surds?

In GCSE Maths, surds are square roots of non-square positive integers, which cannot be simplified to whole numbers. For example, 3 and 5 are non-square integers so square root of 3 and square root of 5 are surds, but 4 is a square integer so square root of 4 is not a surd, because it simplifies to a whole number, 2.

All surds are irrational (they cannot be written as a whole number or as a fraction with whole numbers on top and bottom), which means their decimal forms are never-ending with no recurring patterns. For example square root of 3 equals 1.7320508.... As such, it is easier to leave surds in their exact forms, square root of 3 and square root of 5.

Surds can also include other types of roots that give irrational numbers, such as cube roots like cube root of 2.

Surds revision resources to ace your exams

Surds are covered in our revision notes on Simplifying Surds from GCSE Maths. You can also have a go at our related exam questions and flashcards to test your understanding. Don’t forget to check out the GCSE maths past papers for more general exam revision.

Explore our GCSE Maths revision resources

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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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