1. 10.4 Adding and Subtracting Radical Expressions

2. Simplify radical expressions involving addition and subtraction. Objective 1 Slide 10.4- 2

3. Slide 10.4- 3 Simplify radical expressions involving addition and subtraction. Only radical expressions with the same index and the same radicand may be combined. Expressions such as or cannot be simplified by combining terms.

4. Add or subtract to simplify each radical expression. Slide 10.4- 4 CLASSROOM EXAMPLE 1 Adding and Subtracting Radicals Solution:

5. This expression can not be simplified any further. Slide 10.4- 5 CLASSROOM EXAMPLE 1 Adding and Subtracting Radicals (cont’d) Add or subtract to simplify each radical expression. Solution:

6. Slide 10.4- 6 Simplify radical expressions involving addition and subtraction. Do not confuse the product rule with combining like terms. The root of a sum does not equal the sum of the roots. For example since

7. Add or subtract to simplify the radical expression. Assume that all variables represent positive real numbers. Slide 10.4- 7 CLASSROOM EXAMPLE 2 Adding and Subtracting Radicals with Higher Indexes Solution:

8. Slide 10.4- 8 CLASSROOM EXAMPLE 2 Adding and Subtracting Radicals with Higher Indexes (cont’d) Add or subtract to simplify the radical expression. Assume that all variables represent positive real numbers. Solution:

9. Slide 10.4- 9 CLASSROOM EXAMPLE 2 Adding and Subtracting Radicals with Higher Indexes (cont’d) Add or subtract to simplify the radical expression. Assume that all variables represent positive real numbers. Solution:

10. Perform the indicated operations. Assume that all variables represent positive real numbers. Slide 10.4- 10 CLASSROOM EXAMPLE 3 Adding and Subtracting Radicals with Fractions Solution:

11. Slide 10.4- 11 CLASSROOM EXAMPLE 3 Adding and Subtracting Radicals with Fractions (cont’d) Perform the indicated operations. Assume that all variables represent positive real numbers. Solution: