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Surds: GCSE Maths Definition

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Published

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1 minutes

Contents

  1. 1. What are surds?
  2. 2. Surds revision resources to ace your exams

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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Author
Reviewer
Mark Curtis

Author: 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.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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