This key facts covers What Are Surds? 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 2 of 15 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
What Are Surds?
- Definition: Surds are irrational roots that cannot simplify to whole numbers
- Examples: √2, √3, √5, ∛7 (but NOT √4 = 2 or √9 = 3)
- Why use them? They're exact values (√2 is exact, 1.414... is approximate)
- Irrational: Cannot be written as a fraction a/b
- Infinite decimals: Non-repeating, non-terminating
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 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
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)