Simplify Surds Using Square Factors

Many surds can be simplified using square factors.

You may have met these rules for surds:

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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.