Surds Worksheet

Surds Worksheet

Help your students prepare for their Maths GCSE with this free surds worksheet of 47 questions and answers

  • Section 1 of the surds worksheet contains 36 skills-based surds questions, in 3 groups to support differentiation
  • Section 2 contains 4 applied surds questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 7 foundation and higher level GCSE exam questions on surds 
  • Answers and a mark scheme for all surds questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions created by fully qualified expert secondary maths teachers
  • Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Surds at a glance


Surds are values written as square roots that cannot be further simplified. Surds are used to ensure very exact values are given in calculations. Surds are irrational numbers, if written as decimals, they would go on perpetually with no pattern. If written as fractions irrational numbers cannot have integer numerators or denominators.


We can multiply and divide surds. When multiplying surds, we use the rule “root a multiplied by root b = the root of a multiplied by b”. Similarly, when dividing surds we use the rule “root a divided by root b = the root of a divided by b”. 


We can sometimes simplify surds by taking out factors which are square numbers. We need to keep simplifying the surd until the number under the root sign has no factors which are square numbers.


To add and subtract surds the number under the root sign must be the same. We can only add or subtract two surds with different numbers under the roots if we can simplify one or both of them so that they have the same number under the root. 


Sometimes we might be asked to rationalise the denominator of a fraction. This means finding an equivalent fraction which does not have a surd in the denominator.


Looking forward, students can then progress to additional number worksheets, for example a fractions worksheet or a rounding worksheet.



For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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