I have learned how to simplify radical expressions, as well as changing mixed radicals to entire radicals.

Part 1: How to simplify a radical

As we can see, 135 is not a perfect cube root, but we can simplify this radical by finding a cube root that divides into 135.

First let’s look at some vocabulary :

      

We can see that the index in this example is 3. So the first step is looking through the list that corresponds with the index. In this case it is cube roots.

List of cube roots:

= 1

= 2

= 3

= 4

= 5

= 6

Starting from the top of the list, we can tell that 1 is not going to help, so we move on to the next number which is 8, but that is not a factor of 135 as it doesn’t divide in the number evenly without resulting in a decimal. So we go to the next cube root on the list, which is 27.

27 does divide evenly into 135 which equals 5.

So the radical would look like this :

We can now simplify it by determining the cube root of 27.

= 3

That number now becomes the coefficient of the equation and the 5 remains as the radicand :

=

** Don’t forget to always include the index **

Part 2: How to write a mixed radical as an entire radical.

In this example, we can see that the index is 4, the coefficient is 2 and the radicand is 7.

To be able to turn this into an entire radical, we must be able to put the coefficient (2) back into the root while dragging the index in too.

So we must determine what is and then place that number into the root and multiply both numbers while keeping the index:

 

Therefore, =