Warm Up

1. Preview Warm Up California Standards Lesson Presentation

2. Warm Up Simplify each expression. 1. 14x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + Simplify. All variables represent nonnegative numbers. 4. 5. 6. 15x + 3y 3xy –3a – b + 10

3. California Standards Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

4. Vocabulary like radicals

5. Square-root expressions with the same radicand are examples of like radicals.

6. 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. Helpful Hint Combining like radicals is similar to combining like terms.

8. A. Additional Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

9. the terms are like radicals. Additional Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. C. Combine like radicals. D. Identify like radicals. Combine like radicals.

10. a. b. Check It Out! Example 1 Add or subtract. The terms are like radicals. Combine like radicals. The terms are like radicals. Combine like radicals.

11. Check It Out! Example 1 Add or subtract. c. The terms are like radicals. Combine like radicals. d. Identify like radicals. Combine like radicals.

12. Sometimes radicals do not appear to be like until they are simplified. Simplify all radicals in an expression before trying to identify like radicals.

13. Additional Example 2A: Simplify Before Adding or Subtracting Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

14. Additional Example 2B: Simplify Before Adding or Subtracting Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. The terms are unlike radicals. Do not combine.

15. Additional Example 2C: Simplify Before Adding or Subtracting Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

16. Remember! When you write a radicand as a product, make at least one factor a perfect square.

17. Check It Out! Example 2a Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

18. Check It Out! Example 2b Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. The terms are unlike radicals. Do not combine.

19. Check It Out! Example 2c Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

20. Additional Example 3: Geometry Application Find the perimeter of the triangle. Give the answer as a radical expression in simplest form. Write an expression for perimeter. Factor 20 using a perfect square. Product Property of Square Roots Simplify. Combine like radicals.

21. Find the perimeter of a rectangle whose length is inches and whose width is inches. Give your answer as a radical expression in simplest form. The perimeter is in. Check It Out! Example 3 Write an expression for perimeter 2 (l + w). Multiply each term by 2 . Simplify. Combine like radicals.

22. Lesson Quiz: Part I Add or subtract. 1. 2. 3. Simplify each expression. 4. 5.

23. ft Lesson Quiz: Part II 6. Find the perimeter of the trapezoid. Give the answer as a radical expression in simplest form.