NumberKey Facts

Surd Rules

Part of SurdsGCSE Mathematics

This key facts covers Surd Rules 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 3 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 3 of 14

Practice

14 questions

Recall

22 flashcards

Surd Rules

Operation Rule Example Remember
Multiplication √a × √b = √(ab) √3 × √5 = √15 Multiply under one root
Division √a ÷ √b = √(a/b) √20 ÷ √5 = √4 = 2 Divide under one root
Addition Only like surds 3√2 + 5√2 = 8√2 Can't add √2 + √3
Simplifying Find square factors √12 = √(4×3) = 2√3 Take squares outside
Rationalizing Remove surd from denominator 1/√2 = √2/2 Multiply top and bottom

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 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

Want to test your knowledge?

PrepWise has 14 exam-style questions and 22 flashcards for Surds — with adaptive difficulty and instant feedback.

Join Alpha