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NumberKey Facts

What Are Surds?

Part of Surds — GCSE Mathematics

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 14 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 14

Practice

14 questions

Recall

22 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

Keep building this topic

Read this section alongside the surrounding pages in Surds. That gives you the full topic sequence instead of a single isolated revision point.

The Exact TruthSurd RulesMethod: Simplifying SurdsMethod: Rationalizing the Denominator

Practice Questions for Surds

Which of these is the simplified form of √48?

  • A. 12√2
  • B. 4√3
  • C. 3√4
  • D. 6√2
1 markfoundation

Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.

2 markshigher

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)

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The Exact Truth

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Surd Rules