Exam Questions on Surds

These lessons, with videos, examples and step-by-step solutions, help GCSE Maths students learn about surds by working through some examination questions.

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Surds Exam questions


  1. (a) Write √45 in the form a √5, where a is an integer.
    (b) Express 2(3 + √5)(2 + √5) in the form b + c√5, where b and c are integers.
  2. (a) Expand and simplify (4 + √3)(4 - √3).
    (b) Express 26/(4+√3) in the form a + b√3, where a and b are integers.
  3. (a) Express √108 in the form a√3, where a in an integer.
    (b) Express (2 - √3)2 in the form b + c√3 where b and c integers to be found.
  4. Simplify (3 + √5)(3 - √5)
  5. Simplify (5 - √3)/(2 + √3) giving your answer in the form a + b√3, where a and b are integers.

How to do Surds GCSE A/A* Maths revision?
(simplifying, rationalising)

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