1. Prentice Hall Lesson 11.4 What are like radicals? How do you combine like radicals? BOP:

2. Solution to BOP:

3. 20.DE 6.1; EF 3.6; DF 5.7 22.MN 5.1; NP 3.6; MP = 5 24.TU 7.6; UV 16.5; VT 13.3 26.a.(20, 80), (–40, 30) b.78.1 ft c.(–10, 55) or 55L10 ALGEBRA 1 LESSON 11-3 pages 594–597 Exercises 2.14 4.11.3 6.8.1 8.21.6 10.(–1, 12) 12.(–2, 3) 14. – 2, –1 16. 8, –9 18.9.4 11-3 1212 1212

4. ALGEBRA 1 LESSON 11-3 30.about 9.5 km apart 32.Yes; all sides are congruent. 11-3 34.a.about 4.3 mi b.about 17.4 mi

5. Prentice Hall Lesson 11.4 What are like radicals? How do you combine like radicals? Toolbox: Like radicals in a radical expression have the same radicand. Unlike radicals do not have the same radicand. To simplify sums and differences, use the Multiplication Property of Square Roots to simplify the radical expression(s) as needed. Then use the Distributive Property to combine like radicals and simplify.

6. To simplify products, use the Distributive Property to multiply. (You may use FOIL if both expressions have two terms.) Combine like radicals and simplify. Conjugates are the sum and difference of the same two terms. The product of two conjugates is a difference of two squares. To simplify a quotient, multiply the numerator and denominator by the conjugate of the denominator. Continue to simplify until the resulting expression meets the three requirements for a radical expression in simplest form.

7. A radical expression is in simplest form when it meets the following requirements: 1.The radicand has no perfect-square factors other than 1. 2.The radicand has no fractions. 3.The denominator of a fraction has no radical.

8. Simplify 4 3 + 3. ALGEBRA 1 LESSON 11-4 = (4 + 1) 3Use the Distributive Property to combine like radicals. = 5 3Simplify. 11-4 4 3 + 3 = 4 3 + 1 3Both terms contain 3.

9. 8 5 – 45 = 8 5 + 9 59 is a perfect square and a factor of 45. Simplify 8 5 – 45. ALGEBRA 1 LESSON 11-4 = 8 5 – 9 5Use the Multiplication Property of Square Roots. = 8 5 – 3 5Simplify 9. = (8 – 3) 5Use the Distributive Property to combine like terms. = 5 5Simplify. 11-4

10. Simplify 5( 8 + 9). ALGEBRA 1 LESSON 11-4 5( 8 + 9) = 40 + 9 5Use the Distributive Property. = 4 10 + 9 5 Use the Multiplication Property of Square Roots. = 2 10 + 9 5Simplify. 11-4

11. Simplify ( 6 – 3 21)( 6 + 21). ALGEBRA 1 LESSON 11-4 ( 6 – 3 21)( 6 + 21) = 36 + 126 – 3 126 – 3 441Use FOIL. = 6 – 2 126 – 3(21)Combine like radicals and simplify 36 and 441. = 6 – 2 9 14 – 639 is a perfect square factor of 126. = 6 – 2 9 14 – 63Use the Multiplication Property of Square Roots. = 6 – 6 14 – 63Simplify 9. = –57 – 6 14Simplify. 11-4

12. ALGEBRA 1 LESSON 11-4 = 2( 7 + 3)Divide 8 and 4 by the common factor 4. = 2 7 + 2 3Simplify the expression. = Multiply in the denominator. 8( 7 + 3) 7 – 3 = Simplify the denominator. 8( 7 + 3) 4 11-4 Simplify. 8 7 – 3 = Multiply the numerator and denominator by the conjugate of the denominator. 8 7 – 3 7 + 3

13. A painting has a length : width ratio approximately equal to the golden ratio (1 + 5) : 2. The length of the painting is 51 in. Find the exact width of the painting in simplest radical form. Then find the approximate width to the nearest inch. ALGEBRA 1 LESSON 11-4 11-4 Define:51 = length of painting x = width of painting Relate: (1 + 5) : 2 = length : width Write: = x (1 + 5) = 102Cross multiply. = Solve for x. 102 (1 + 5) x(1 + 5) (1 + 5) 51 x (1 + 5) 2

14. ALGEBRA 1 LESSON 11-4 (continued) x = Multiply in the denominator. 102(1 – 5) 1 – 5 x =Simplify the denominator. 102(1 – 5) –4 x = Divide 102 and –4 by the common factor –2. – 51(1 – 5) 2 x = 31.51973343 Use a calculator. x 32 The exact width of the painting is inches. The approximate width of the painting is 32 inches. – 51(1 – 5) 2 11-4 x = Multiply the numerator and the denominator by the conjugate of the denominator. (1 – 5) 102 (1 + 5)

15. 16 5 – 7 Simplify each expression. 1.12 16 – 2 162. 20 – 4 53. 2( 2 + 3 3) 4.( 3 – 2 21)( 3 + 3 21)5. ALGEBRA 1 LESSON 11-4 40–2 52 + 3 6 –123 + 3 7 –8 5 – 8 7 11-4

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