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Surds

Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency exam topic, so students should expect to explain it clearly under timed conditions.

Study this topic

1

The Exact Truth

Introduction2

What Are Surds?

Key Facts3

Surd Rules

Key Facts4

Method: Simplifying Surds

Deep Dive5

Method: Rationalizing the Denominator

Deep Dive6

Visual Understanding

Diagram7

Worked Example 1: Simplifying

Notes8

Worked Example 2: Adding Surds

Notes9

Worked Example 3: Multiplying Surds

Notes10

Worked Example 4: Rationalizing

Notes11

Worked Example 5: Expanding with Surds

Notes12

Higher Level: Complex Rationalization

Deep Dive13

Common Mistakes to Avoid

Exam Tips14

Exam Tips

Exam Tips

Sample 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

Sample Questions

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

14

exam-style questions

22

revision flashcards

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