Edexcel International GCSE Mathematics A · 4MA1
Surds
A surd keeps an irrational root exact instead of replacing it with a rounded decimal. Simplifying involves extracting square factors. Like surd terms can be collected only when their remaining root parts match.
Key method
For non-negative a and b, √(ab) = √a × √b. Search for the largest square factor first. Rationalising a denominator multiplies numerator and denominator by a suitable root.
Worked example
Simplify √72 + √8.
- Write √72 = √(36 × 2) = 6√2.
- Write √8 = √(4 × 2) = 2√2.
- Add the coefficients of the matching √2 terms.
Answer and interpretation
8√2.
Common mistake
√72 + √8 is not √80: square roots do not distribute over addition.
Practise independently
Rationalise 3/√5.
Check your answer
Multiply by √5/√5 to obtain 3√5/5.
Syllabus connection
This lesson develops surds within the number area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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