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Square Root - GCSE Maths Definition

Reviewed by: Mark Curtis

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What is a square root?

The square root of a number is a value which, when multiplied by itself, gives you that number. For example, a square root of 16 is 4, because 4 cross times 4 equals 16. The negative of 4, i.e. negative 4, is also a square root of 16, because open parentheses negative 4 close parentheses cross times open parentheses negative 4 close parentheses equals 16 (multiplying two negatives gives a positive).

Every number (except zero) has a positive and a negative square root. The positive square root of a number is given its own symbol, square root of blank end root. The negative square root of a number is not given its own symbol, but can be written as negative square root of blank end root. A quick way to write both square roots is plus-or-minus square root of blank end root, called a plus-or-minus square root. An example is given below.

Type

Example

Positive square root

square root of 16 equals 4

Negative square root

negative square root of 16 equals negative 4

Both square roots

plus-or-minus square root of 16 equals plus-or-minus 4

Square root revision resources to ace your exams

Square roots are covered in our revision notes on Powers, Roots & Indices 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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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths Content Creator

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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