1. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Warm Up Simplify each expression. 1. 14x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + 15x + 3y 3xy –3a – b + 10

2. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Warm Up Continued Simplify. All variables represent nonnegative numbers. 4. 5. 6.

3. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Add and subtract radical expressions. Objective

4. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions like radicals Vocabulary

5. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Square-root expressions with the same radicand are examples of like radicals.

6. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done: Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.

7. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Combining like radicals is similar to combining like terms. Helpful Hint

8. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Directions: Add or subtract Remember: Look for “like” radicals

9. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 1 A. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

10. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 1 Continued… C. D. Identify like radicals. Combine like radicals. the terms are like radicals.

11. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 2 The terms are like radicals. a. b. The terms are like radicals.

12. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 2 Continued… c. The terms are like radicals. d. The terms are like radicals. Combine like radicals.

13. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Sometimes radicals do not appear to be like until they are simplified, Simplify all radicals in an expression before trying to identify like radicals.

14. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Directions: Simplify, then add or subtract

15. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 3 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

16. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 4 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

17. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions When you write a radicand as a product, make at least one factor a perfect square. Remember!

18. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 5 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

19. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Example 6 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

20. Holt Algebra 1 11-7 Adding and Subtracting Radical Expressions Lesson Summary Add or subtract. 1. 2. Simplify each expression. 3.