| 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 |
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.
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