NumberDiagram

Visual Understanding

Part of SurdsGCSE Mathematics

This diagram covers Visual Understanding 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 6 of 14 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 6 of 14

Practice

14 questions

Recall

22 flashcards

Visual Understanding

Simplifying Surds

√50 = ?
50 = 25 × 2
√50 = √(25×2)
= √25 × √2
= 5√2

Always find largest square!

Like Surds

Can add: 2√3 + 5√3 = 7√3
(like 2x + 5x = 7x)

Can't add: √2 + √3
(different surds)

First simplify, then combine!

Difference of Squares

(a + √b)(a - √b) = a² - b

Example:
(3 + √2)(3 - √2)
= 9 - 2
= 7

No surd in answer!

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.

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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