1. Number Systems-Part 8

2. Adding and Subtracting Radical Expressions
You can add and subtract radical expressions if the indexes are the same and the numbers under the radical symbol are the same.

3. Adding Radical Expressions
When you add radical expressions, add the coefficients.

4. Examples
First, check to make sure the radicals have the same index. No index is written in either of these expressions, so the index in both of them is two. Next, check if both radical expressions have the same quantity under the radical sign. Both expressions have the number 3 under the radical sign.

5. Examples

6. Subtracting Radical Expressions
Subtraction follows the same rules. You can also simplify radical expressions when a variable is found under the radical symbol.

7. Fractions and Roots
If you are given a fraction under a square root, it is the same as taking the square root of the numerator and the square root of the denominator.

8. Example

9. Caution! Major Mistake Territory!
Radicals without the same index cannot be added or subtracted. Radicals without the same number under the radical symbol cannot be added or subtracted.