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Prentice Hall Lesson 11.4 What are like radicals? How do you combine like radicals?

Learn how to combine like radicals in algebraic expressions by simplifying and using the Multiplication and Distributive Properties step by step.

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Prentice Hall Lesson 11.4 What are like radicals? How do you combine like radicals?

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

  2. Solution to BOP:

  3. ALGEBRA 1 LESSON 11-3 pages 594–597  Exercises 2. 14 4. 11.3 6. 8.1 8. 21.6 10. (–1, 12) 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 1 2 1 2 • (–2, 3) • 14. – 2 , –1 • 16. 8 , –9 • 18. 9.4 11-3

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

  5. Prentice Hall Lesson 11.4What 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: • The radicand has no perfect-square factors other than 1. • The radicand has no fractions. • The denominator of a fraction has no radical.

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

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

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

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

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

  13. ALGEBRA 1 LESSON 11-4 Define: 51 = length of painting x = width of painting Relate: (1 + 5) : 2 = length : width (1 + 5) 2 Write: = x (1 + 5) = 102 Cross multiply. = Solve for x. 51 x 102 (1 + 5) x(1 + 5) (1 + 5) 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. 11-4

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

  15. ALGEBRA 1 LESSON 11-4 Simplify each expression. 1. 12 16 – 2 16 2. 20 – 4 5 3. 2( 2 + 3 3) 4. ( 3 – 2 21)( 3 + 3 21) 5. –2 5 2 + 3 6 16 5 – 7 –123 + 3 7 –8 5 – 8 7 40 11-4

  16. Summary: Don’t forget to write your minimum three sentence summary answering today’s essential question here!

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