Simplify a surd
- Find a square factor.
- Split the root.
- Simplify the square root.
Answer: √72 = 6√2
🔢 Number
Surds
Learn surds with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Surds is part of advanced topics and appears often in KS3–GCSE maths.
- Surds are exact irrational roots left in root form.
- Use the worked model, help guide, interactive question and flashcards to practise surds until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Surds learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Surds
- Learn the rule: Surds are exact irrational roots left in root form.
- Worked model: Find a square factor. Split the root. Simplify the square root.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
Simplify √50.
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Surds
BackSurds are exact irrational roots left in root form.
FrontExample answer: Simplify √50.
Back√50 = √(25 × 2) = 5√2.
FrontCommon check for Surds
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.