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This lesson covers surds — irrational numbers that are left in root form — for AQA GCSE Mathematics Higher Tier. Surds provide exact values where decimals would be rounded approximations. You need to be able to simplify surds, perform operations with them, and rationalise denominators.
A surd is a root that cannot be simplified to a whole number or a fraction. It is an irrational number — its decimal form goes on forever without repeating.
| Expression | Surd? | Reason |
|---|---|---|
| Square root of 2 | Yes | 1.41421356... (irrational) |
| Square root of 9 | No | Equals 3 (rational) |
| Square root of 5 | Yes | 2.23606797... (irrational) |
| Square root of 100 | No | Equals 10 (rational) |
| Cube root of 7 | Yes | 1.91293118... (irrational) |
| Square root of 16/25 | No | Equals 4/5 (rational) |
Exam Tip: The question will usually say "give your answer in surd form" or "give an exact answer". This means do NOT use a calculator to find a decimal — leave roots in your answer.
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