This section introduces two types of radicands with variables and covers how to simplify them... or not.

You can watch a video on this content below:

There are two main types of radicands we wish to distinguish here.

We saw in the previous section how to simplify radicals where the radicand is entirely numeric. Obviously numeric radicals can always be made into type one radicals (if you have a radical that looks like two constants being added or subtracted, simply perform the addition or subtraction until the radicand is a single number). Typically the best way to deal with numeric radicals is to simplify them as far as possible in order to determine what kind of simplification we can do in the overall expression or equation where the radical is found.

Since numeric radicals can always be forced into being a type one radical, the real difficulty only begins when we are using non-numeric radicals; specifically radicals where the radicand includes variables.

Radicands with Variables

We have determined how to tackle radicals when they have purely numeric radicands, but what do we do when our alphabet starts making appearances in the radicand? As one might expect, things get more difficult, although perhaps not always for the reasons one might think.

It is worth a note that radical expressions should be treated as an unbreakable ‘term’ when they are separated by addition or subtraction. Thus the only way to put two radical expressions together that are separated by addition or subtraction is if they are exactly the same radical expression. Consider the following example:

In the next two tiles we will look at what we can do with Type 1 and Type 2 radicals individually, and then we will discuss how to deal with more complex equations that may have one or both of these types at the same time.