Mathematics (9-1) - 0980 CIE

Surds

Overview

A surd is a root that cannot be simplified to a whole number, such as \(\sqrt{2}\) or \(\sqrt{5}\). Surds let you keep answers exact rather than rounding, which matters whenever a question asks for an exact value, and they are the natural language of Pythagoras and trigonometry results.

In this lesson (Extended tier) you will simplify surds, multiply and add them where possible, and rationalise a denominator so that no surd is left underneath a fraction. These techniques keep working tidy and answers exact.

Objectives

Understand and use surds, including simplifying expressions.
Rationalise the denominator.

Audio Lesson

Listen to this lesson in the app

Mind map

This topic is mapped out so you can see how the ideas connect.

Open the mind map in the app

Flashcards

Quick recall practice on the facts this topic is tested on.

Practise these cards in the app

Lesson Note

Writing \(\sqrt{50}\) as \(5\sqrt{2}\) is both neater and exact, and leaving an answer as a surd avoids the rounding error a decimal would introduce. Surds appear throughout geometry and trigonometry, so handling them confidently keeps later work exact.

Complete Note Available on the Green Bridge App

Get the Green Bridge CBT app on your phone or computer for the complete IGCSE library: past papers, mark schemes, mind maps, flashcards and audio lessons.

Full lesson notes with diagrams

AI-powered learning assistant

Timed mock exams marked the moment you finish

Download Mobile App Download Desktop App

Available on Android, Windows, macOS, and Linux iOS app coming soon

Lesson Evaluation

Congratulations on completing the lesson on Surds. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

Simplify √50. A. 5√2 B. 2√5 C. 25√2 D. 10√5 Answer: A
Work out √3 x √12. A. √15 B. 6 C. 36 D. 4√3 Answer: B
Simplify 2√5 + 3√5. A. 5√10 B. 6√5 C. 5√5 D. 5 Answer: C
Rationalise the denominator of 1/√2. A. √2 B. 2/√2 C. √2/2 D. 1/2 Answer: C
Which expression cannot be simplified? A. √8 B. √2 + √3 C. √2 x √8 D. 4√3 - √3 Answer: B

Work through these questions in the app