O LevelMathsCambridgeRevision NotesNumberSurdsSimplifying Surds

Simplifying Surds (Cambridge O Level Maths)

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Surds & Exact Values

What is a surd?

  • A surd is the square root of a non-square integer
  • Using surds lets you leave answers in exact form
    • e.g. 5 square root of 2  rather than 7.071067812

Surd and not surd, A Level & AS Level Pure Maths Revision Notes

How do I calculate with surds?

  •  Multiplying surds
    • You can multiply numbers under square roots together
    • eg. square root of 3 space cross times space square root of 5 space equals square root of space 3 cross times 5 space end root equals space square root of 15
  • Dividing surds
    • You can divide numbers under square roots
    • eg. square root of 21 space divided by space square root of 7 equals space square root of 21 space divided by space 7 space end root equals space square root of 3
  • Factorising surds
    • You can factorise numbers under square roots
    • eg. square root of 35 space equals square root of 5 space cross times space 7 space end root equals space square root of 5 space cross times square root of 7
  • Adding or subtracting surds is very like adding or subtracting letters in algebra – you can only add or subtract multiples of “like” surds
    • eg. 3 square root of 5 plus space 8 square root of 5 space equals space 11 square root of 5 space o r space 7 square root of 3 space – space 4 square root of 3 space equals space 3 square root of 3
    • Be very careful here, you can not add or subtract numbers under square roots
    • Think about square root of 9 space end root plus space square root of 4 equals space 3 space plus space 2 space equals space 5 
      • It is not equal to square root of 9 plus 4 end root space equals space square root of 13 space equals space 3.60555 horizontal ellipsis

Examiner Tip

  • If you are working on an exam question and your calculator gives you an answer as a surd, leave the value as a surd throughout the rest of your calculations to make sure you do not lose accuracy throughout your questions

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    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.