Simplifying radicals containing variables

Special care must be taken when simplifying radicals containing variables. We will start with perhaps the simplest of all examples and then gradually move on to more complicated examples . Take a look at the following radical expressions. 

Do you understand how we got the answer? Do not worry if you do not! you will know how by the time you finish reading this lesson.

Let us look at a few examples in this form. If x = 3 or x = 5, then we have

Now, let us look at an example where x is a negative number. Let x  = -6

Now what about the cube root of x? The cube root of x will behave a little differently. 

If x  = 2 or x = -2, the answer is not always positive.

As you can see here, the answer is always x

Interesting or challenging examples of simplifying radicals containing variables

Example #1:

Simplify the following radical expression.

The trick is  to  write  the  expression  inside  the  radical as 

Then, 

We will need to use some properties of exponents to do this. 

Notice that something is equal to 8y⁸

Let us now conclude this lesson with the last example below

 Try  to  write  the  expression  inside  the  radical as 

Then,

Therefore,