Surds
Surds are irrational numbers left in root form. Students must simplify, add, subtract, multiply and rationalise surds, skills that also prepare them for further study in mathematics.
What You'll Learn
- Simplifying surds by extracting square factors
- Adding and subtracting like surds
- Multiplying and dividing surds
- Rationalising the denominator of a fraction
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Thinking the square root of a + b equals the square root of a plus the square root of b
Forgetting to simplify fully (e.g., leaving root 8 instead of 2 root 2)
Errors when expanding brackets containing surds
What Examiners Say About Surds
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
For time intervals crossing midnight, split into two parts: time until midnight + time after midnight. Remember an hour has 60 minutes, not 100.
Source: CIE 0580 · Feb/March 2024 · Paper 1 · Q5
- Common Mistake●●●●●
For compound interest, the rate and the number of periods must MATCH. 0.25% per month over 5 years = 60 monthly periods (not 5). Don't silently convert to annual — apply the rate as given.
Source: CIE 0580 · Feb/March 2023 · Paper 4 · Q1a(iii)
- Common Mistake●●●●●
When finding bounds, always give the final answer in the SAME UNITS as the variable in the question. If l is in metres, bounds must be in metres — convert at the end if your working was in cm.
Source: CIE 0580 · May/June 2023 · Paper 1 · Q18
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
Useful for this topic:
Related Topics
Indices and Powers
Index laws are a key algebra and number skill. Students must also handle negative indices, making this a topic that bridges number work with algebraic manipulation.
Pythagoras' Theorem
Pythagoras' theorem relates the three sides of a right-angled triangle and is one of the most practical geometry topics at Cambridge IGCSE. It is used in 2D and 3D problems, coordinate geometry, and combined with trigonometry.
Quadratic Equations
Quadratic equations are a significant step up from linear equations. Students need to factorise, complete the square, and use the quadratic formula to find solutions.
Related Articles
How to Read an Examiner Report (And Actually Use It)
Cambridge publishes a free examiner report for each IGCSE maths series, showing where students lost marks. Here is how to use them for targeted revision.
Online LearningTop 10 Online Maths Learning Platforms for Kids
Online math learning platforms have revolutionized how kids approach numbers and equations. These interactive tools make math fun, engaging, and accessible for
Maths EducationVirtual Reality Maths: Immersive Learning Experiences for the Digital Age
Imagine stepping into a 3D world where numbers come alive and equations float in mid-air. Virtual Reality (VR) is revolutionizing how students learn maths, maki
Ready to Master Surds?
Take our free diagnostic quiz to find out exactly where you stand, then practise number with our AI tutor.
Key number facts, rules, and formulae at a glance