This week in pre-calc 11 I learned how to add and subtract radicals. I think adding and subtracting radicals is an important skill to have because it makes working with radicals easy at the end of the equation. To start, we need to know that radicals are treated the same as variables in this lesson, now if we have 2x + 3y + 3x  we get 5x + 3y, this is because only the x’s can be added together since they are the same. to start easily, since we know how to add variables, we can get into adding radicals.

Like variables, radicals that have the SAME radicand go together. here is an example.

Now as you can see we only added the coefficients together, you do not touch the radicand, that is just there for you to know which numbers go together.

The same case goes for subtracting radicals. Numbers with the same radicand go together. Here is an example.

However, if we have something like √18 – √8  the roots are the same (both are square roots), but the radicands are different. We’ll start by simplifying each radical. √18 can be simplified to √(9 * 2), and since 9 is a perfect square, it simplifies to 3. So, √18 becomes 3√2. Similarly, √8 simplifies to √(4 * 2), which is 2√2. Now, we have 3√2 – 2√2. Since they have the same root and radicand, we can simply subtract the coefficients: (3 – 2)√2 = √2. So, √18 – √8 simplifies to √2.