1. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 Algebra 2 Lesson 7-3 (Page 374)

2. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 To add and subtract radical expressions.

3. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 Like radicals are radical expressions that have the same index and the same radicand.

4. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Add or subtract if possible. a. 7 xy + 3 xy Distributive Property 7 xy + 3 xy = (7 + 3) xy = 10 xy Subtract. 33 b. 2 x – 2 5 The radicals are not like radicals. They cannot be combined. 7-3

5. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Add or subtract if possible. 7-3 a. 42 b. c. d.

6. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Add or subtract if possible. 7-3 a. b. c. d. cannot combine

7. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Add or subtract if possible. 7-3 a. b. c. 20xy d. 9xy

8. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 The rectangular window shown below is made up of three equilateral triangles and two right triangles. The equilateral triangles have sides of length 4 feet. What is the perimeter of the window? So the window’s height is 2 3 ft. The length of the window is 8 ft. The perimeter is 2(2 3 + 8) ft or 16 + 4 3 ft. The height of an equilateral triangle with side length 4 ft is 2 3 ft. 7-3

9. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 Find the perimeter of the window if each small square is 6 in. on a side. a. in. or about 101.8 in. b. about 101.8 sq. in. c. 72 in. d. 576 sq. in.

10. Simplify 3 20 – 45 + 4 80. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 3 20 – 45 + 4 80 = 3 2 2 5 – 3 2 5 + 4 4 2 5Factor each radicand. Simplify each radical.= 3 2 5 – 3 5 + 4 4 5 Multiply.= 6 5 – 3 5 + 16 5 Use the Distributive Property.= (6 – 3 + 16) 5 = 19 5 7-3

11. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 a. b. 2 c. d.

12. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 To multiply and divide binomial radical expressions.

13. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Multiply (2 + 4 3)(1 – 5 3). Use FOIL. (2 + 4 3)(1 – 5 3) = 2 1 – 2 5 3 + 4 3 1 – 4 3 5 3 = 2 + (4 – 10) 3 – 60Distributive Property = –58 – 6 3 7-3

14. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 a. –1 b. c. d. 1

15. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Multiply (3 + 7)(3 – 7). = 9 – 7 = 2 (a + b)(a – b) = a 2 – b 2 (3 + 7)(3 – 7) = 3 2 – ( 7) 2 7-3

16. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 a. b. c. 9 d. 3

17. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 Rationalize the denominator of 2 – 3 4 + 3 2 – 3 4 + 3 = 2 – 3 4 + 3 4 – 3 4 – 3 is the conjugate of 4 + 3.= 2 – 3 4 + 3 4 – 3 Multiply. 4 2 – ( 3) 2 8 – 2 3 – 4 3 + ( 3) 2 = Simplify. 11 – 6 3 13 = 7-3

18. Binomial Radical Expressions ALGEBRA 2 LESSON 7-3 7-3 Rationalize the denominator of. a. b. c. d.