How do we simplify radical expressions?

How do we simplify radical expressions?

Radical expressions look like this:

√108y³

Now when you see that your just like o.O

But it's not that hard as it's made to look, you just have to know how to solve it. 

Just like you'd do when you just have a normal radical like √108 , you first separate the biggest square and number that could multiply to that number under the radical. 

So for √108:

√36 * √3

36 is a perfect square and is the biggest one that fits into 108.

So in this case since you still have variables, don't forget to simplify those before you jump to let's say √36 * √3 = 6√3

We have y³, so we'd have to look for the greatest squared number.

Which in this case would be y².

That leads to √y² * √y

So lets put everything together.

√36 * √3 * √y² * √y

Now is when we can simplify and put numbers and variables outside of the radical. 

36 and y² are both prefect squares, which would go outside of the radical. 3 and y would stay inside the radical since they're not prefect squares. It would look something like this:

Since √36 = 6

and

√y² = y

↓

The outside would be 6y.

And since the 3 and y are simplified as they're gonna get, they stay the same. 

Your result would be:

6y√3y

Note:  The examples shown in these lessons on radicals show ALL of the steps in the process.  It mayNOT be necessary for you to list EVERY step.  As long as you understand the process and can arrive at the correct answer, you are ALL SET!!

Sources:

1. John Schnatterly: johnschnatterly.blogspot.com
2. http://www.regentsprep.org/Regents/math/ALGEBRA/AO1/Lsimplify.htm