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The Exact Truth

Part of Surds · GCSE GCSE Mathematics revision

This introduction covers The Exact Truth 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 1 of 15 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 15

Practice

14 questions

Recall

22 flashcards

The Exact Truth

When ancient Greek mathematicians discovered that the diagonal of a unit square has length √2, they found a number that couldn't be written as a fraction. This discovery shook mathematics! Today, we keep these 'irrational' numbers in their exact root form - called surds - because they're more precise than any decimal approximation. Engineers use surds for exact calculations in bridge designs, physicists for quantum mechanics, and even your phone's GPS calculations involve surds.

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.

What Are Surds?Surd RulesMethod: Simplifying Surds

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 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

14 questions on Surds — practise free

Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.

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