Maths Resources GCSE Worksheets


Rationalise The Denominator Worksheet

Rationalise The Denominator Worksheet

Help your students prepare for their Maths GCSE with this free rationalise the denominator worksheet of 38 questions and answers

  • Section 1 of the rationalise the denominator worksheet contains 27 skills-based rationalise the denominator questions, in 3 groups to support differentiation
  • Section 2 contains 3 applied rationalise the denominator questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 8 foundation and higher level GCSE exam questions
  • Answers and a mark scheme for all rationalise the denominator 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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Rationalise the denominator at a glance


Surds are the square roots of numbers that cannot be simplified. They are used to write irrational numbers precisely for the sake of accuracy in calculations. When surds are written as decimals, they go on forever without any pattern. Irrational numbers cannot be written as fractions with integer numerators and denominators.


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. To rationalise the denominator of a fraction which has one term involving a surd as the denominator, we multiply the numerator and denominator of the fraction by the surd.


To rationalise the denominator when the denominator is made up of a surd and a rational number, we multiply both the numerator and the denominator of the fraction by the conjugate of the denominator. The conjugate is found by changing the sign between the two terms.


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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