Week 4 : Simplifying And Adding Radicals

Hi guys,Today i will tell you about the Simplifying and Adding radicals.

So let’s start with the first example :

Adding : 2\sqrt{11} + 8\sqrt{11}

So we can know : the two radicals inside the roots. they have same the number “11”. This means you can combine them but only combine the number before the roots. We will still keep the radicals inside roots

Let’s go to another example :

8\sqrt{5} + \sqrt{3} + 3\sqrt{5} + 10\sqrt{3}

So with this example we can not adding with diffirent radicals. First, I always sort the number have same radicals are next to each other. Then we will adding each number have the same radicals. We will get like this :

8\sqrt{5} + 3\sqrt{5} + \sqrt{3} + 10\sqrt{3}= 11\sqrt{5} + 11\sqrt{3}

Just remember, never do combine the number have diffirent radicals like
8\sqrt{5} + \sqrt{3} and then get 9\sqrt{8} . It is the big mistake if you combine it together.

This is not correct because \sqrt{5} and \sqrt{3} are not same radicals so we can not be added them together.