Surds — GCSE Mathematics Revision
Revise Surds for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Rounding & EstimationWhat is Surds?
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3. You can add and subtract like surds (2√3 + 5√3 = 7√3) but not unlike surds. Rationalise the denominator by multiplying top and bottom by the surd: 1/√3 = √3/3.
Step-by-step explanationWorked example
Simplify √50 + √8. √50 = √(25×2) = 5√2. √8 = √(4×2) = 2√2. So √50 + √8 = 7√2.
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Common mistakes
- 1Trying to add unlike surds: √2 + √3 ≠ √5.
- 2Not fully simplifying — √18 should become 3√2, not left as √18 or simplified only to √(9×2).
- 3Forgetting to rationalise the denominator when the question requires an exact answer.
- 4Errors when expanding (a + √b)(a - √b) — this is the difference of two squares pattern.
Surds exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Surds
Core concept
A surd is an irrational root that cannot be simplified to a whole number, like √2 or √5. Simplify surds by finding the largest square factor: √12 = √(4×3) = 2√3. You can add and subtract like surds (2…
Frequently asked questions
What does rationalise the denominator mean?
It means rewriting a fraction so there is no surd in the denominator. Multiply the top and bottom by the surd (or by the conjugate if the denominator is a + √b).
Are surds on the Foundation tier?
Basic surd simplification appears on some Foundation papers, but most surd work (rationalising, expanding) is Higher tier only.