  # Simplify Surds Using Square Factors

In this worksheet, students will simplify surds into multiples of square roots and square factors. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Number, Indices and Surds

Curriculum subtopic:   Structure and Calculation Exact Calculations

Difficulty level:   #### Worksheet Overview

Many surds can be simplified using square factors.

You may have met these rules for surds:  Let's look at an example now.

Using these rules means that we can write:

e.g. We can now take this one step further: We will need to look for square factors of any surd we are asked to simplify.

Here is another example.

e.g. Simplify: We need to think about the factors of 20.

They are 1 x 20, 2 x 10 and 4 x 5.

We know that 4 is a square number and so it would be helpful to rewrite √20 as 4 x 5.

So we can simplify as follows: In this activity, we will simplify surds into multiples of square roots.

This will be a useful skill to support your mental maths and problem solving in all areas of maths.

You may want to have a pen and paper handy so that you can record your working and compare these to our examples written by a teacher.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started 