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This lesson covers simplifying surds, adding and subtracting surds, multiplying surds, expanding brackets involving surds, and rationalising the denominator. Surds is a Higher-tier only topic in the Edexcel GCSE Mathematics (1MA1) specification and frequently appears on Papers 1, 2 and 3.
| Term | Meaning |
|---|---|
| Surd | An irrational root that cannot be simplified to a whole number, e.g. √2, √5 |
| Rational number | A number that can be written as a fraction p/q where p, q are integers and q ≠ 0 |
| Irrational number | A number that cannot be written as a fraction — its decimal goes on forever without repeating |
| Rationalise the denominator | Rewrite a fraction so that the denominator contains no surds |
| Conjugate | The expression formed by changing the sign between two terms, e.g. the conjugate of (3 + √2) is (3 - √2) |
A surd is a root that cannot be simplified to a rational number.
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