So, in the last blog post we talked about exponents in radicals and how we can use them to solve or simplify the Radical.

Today we are going to see how to Add or Subtract the Radicals-

So for introduction we are going to see a mixed Radical and label the things that are important.

As you can see , there are three main components  Radicand, Index, and Coefficient. 

Therefore to add or subtract two radicals we need to have the same Radicand, or else you cannot add or subtract them.

If you have the same Radicand then you just Add or Subtract the Coefficient.

Also you do not Add or Subtract the radicand or the index, they stay in the same position and are not touched.

 

Lets look at some example of Addition and Subtraction–

Addition- 

So, with the help of this example we can see that the Coefficient ADD or Subtract not the radicand or the index.

We saw that we have the same Radicand, so we just add the coefficient and YAAYY! We got the answer.

Subtraction- 

Same with Subtraction.

We saw that we have the same Radicand, so we just subtract and again YAAYY! We got the answer.

 

Now let’s see how can do the same thing with the entire and how we can Add or Subtract them.

To add or subtract the entire radical we first have to convert it into a mixed radical which we learned in the first unit using factor tree.

Lets look at some examples-

Addition- 

1. Here we first changed the entire Radical into mixed by using factor tree.
2. Then simplified the mixed radical even more and now we have the same Radicand on both sides.
3. Now, we just add the Coefficient.

Subtraction- 

1. Here we just do the same thing we did with Addition.
2. So, we first changed the entire Radical into mixed by using factor tree.
3. Then simplified the mixed radical even more and got the same Radicand on both sides.
4. Now,  just subtract the Coefficient.

 

Thats it, you now know how to add or subtract Mixed and Entire Radicals.