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GCSE Maths: Surds

Practise GCSE Higher Maths surds — simplifying, rationalising the denominator and expanding surds. Targeted AQA, Edexcel, OCR and Eduqas questions.

NumberHigher tierAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on surds, and what each one is really asking.

Simplifying surds
Adding and subtracting surds
Multiplying and dividing surds
Rationalising the denominator
Expanding brackets with surds

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • √a × √b = √(ab)
  • Always simplify surds by finding perfect square factors
  • To rationalise 1/√n, multiply top and bottom by √n

Surds questions students ask

How do I simplify a surd?

Find the largest perfect square that is a factor of the number under the root. E.g. √48 = √(16×3) = 4√3.

What does rationalising the denominator mean?

It means eliminating surds from the denominator of a fraction. Multiply numerator and denominator by the surd (or conjugate for expressions like a + √b).