This key facts covers Surd Rules within Surds for GCSE Mathematics. Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 15 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Surd Rules
| Operation | Rule | Example | Remember |
|---|---|---|---|
| Multiplication | √a × √b = √(ab) | √3 × √5 = √15 | Multiply under one root |
| Division | √a ÷ √b = √(a/b) | √20 ÷ √5 = √4 = 2 | Divide under one root |
| Addition | Only like surds | 3√2 + 5√2 = 8√2 | Can't add √2 + √3 |
| Simplifying | Find square factors | √12 = √(4×3) = 2√3 | Take squares outside |
| Rationalizing | Remove surd from denominator | 1/√2 = √2/2 | Multiply top and bottom |
Practice questions for Surds
Which of these is the simplified form of √48?
Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.
Quick recall flashcards
What is a surd?
An irrational root that cannot be simplified to a whole number
Examples: √2, √3, √5, ∛7
NOT surds: √4 = 2, √9 = 3 (these simplify to whole numbers)
What are Like Surds?
Surds with the same root part
Examples of like surds:
• 3√2 and 5√2 (both have √2)
• 2√7 and -4√7 (both have √7)
Can add/subtract like surds:
3√2 + 5√2 = 8√2