Surds

Study and Revision Guide

A number that cannot be square rooted exactly is called a surd. Square roots of 2, 3, 5, in fact square roots of all prime numbers are surds. They give decimals that never repeat and never end.

Here are a few examples:

root 2

root 3

Some calculators such as the Casio FX-85ES can work with surds and are useful for checking and working with surds.

 

In these tutorials you are shown how to work with surds.

 

Rules for Surds

Firstly, you will need to be able to simplify a surd by using the multiplication rule.

For example

examples

These answers can be seen in this video tutorial: the multiplication rule for surds

 

You are then going to need to know how to combine surds by addition, subtraction and multiplication.

For example

examples

These answers can be seen in this video tutorial: combining surds

 

Then you will need to look at simplifying the division of surds

For example

example

This answer and others can be seen in this video tutorial: the division rule for surds

 

You will also need to know how to rationalise a fraction

For example

examples

These answers and others can be seen in this video tutorial: rationalising surds

Exam Questions on Surds with Video Worked Solutions

The following questions will help with your maths revision, they are on surds and taken from past examination question papers.

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