Addition and subtraction of surds

This article continues from a previous article. In this article we shall explore how to add and subtract surds. Just like any other forms of numbers we can add and subtract surds. But there are a few simple rules that you must remember.

• To add or subtract surds they must be in their simplest form
• We can only add or subtract like surds

You can think of the second rule above this way. You can only add objects of the same type;
We can add apples of the same type to get a number of apples;

Similarly to bananas we can add or subtract to get a number of bananas.

But we cannot add a banana and an apple to get a single number of objects;

Example

Evaluate;

We have to add the expression. Remember to add or subtract we must write each surd in it’s simplest form.


…therefore;

Adding and subtracting surds can be treated in the same way you treat algebraic expressions. For example;

We can use the same idea to add or subtract surds where;

Remember we can only add or subtract like surds only. The following two expressions cannot be added directly.

We will need to simplify the expressions before we can add them.

Example

Evaluate;

We know that;

…therefore;

Notice that we have to rewrite the expression to get similar surds in both terms.

Example

Evaluate;

In this example we will need to simplify each term and write it in terms of √2. So we have;

Below are more examples of adding and subtracting surds.