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Simplify Surds Using Square Factors

In this worksheet, students will simplify surds into multiples of square roots and square factors.

'Simplify Surds Using Square Factors' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

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

Curriculum topic:   Number, Indices and Surds

Curriculum subtopic:   Structure and Calculation Exact Calculations

Popular topics:   Square Numbers worksheets

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:



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. 

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