Surds - GCSE Maths Definition

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 and are surds, but 4 is a square integer so is not a surd, because it simplifies to a whole number, .

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 . As such, it is easier to leave surds in their exact forms, and .

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

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.

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