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Warm-up

Warm-up. 1.√x 2. 2.√z 10. 3.√y 4. 4.√a 7. 5.√k 3. = y 2. = k√k. = x. = z 5. = a 3 √a. 1. √x 4 y 6. 2. √x 5 y 7. = x 2 y 3. = x 2 y 3 √xy. 3, √x 5 y 10. 4. √81x 6 y 3. = x 2 y 5 √x. = 9x 3 y√y. 2.). 4.). 4√3 x 3√5. 9√2 x 2√3. √2 x √3. 1.). 3.). √5 x √2.

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Warm-up

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  1. Warm-up 1.√x2 2.√z10 3.√y4 4.√a7 5.√k3 = y2 = k√k = x = z5 = a3√a 1. √x4y6 2. √x5y7 = x2 y3 = x2y3√xy 3, √x5y10 4. √81x6y3 = x2y5√x = 9x3y√y

  2. 2.) 4.) 4√3 x 3√5 9√2 x 2√3 √2 x √3 1.) 3.) √5 x √2 Multiplication of radicals = √6 = √10 = 12√15 = 18√6

  3. 2 4 2 12 2 3 √4 x √6 1.) Multiplication of radicals = √24 = 2√6 2√2x3

  4. Simplifying Radicals using thedistributive property

  5. Warm-up

  6. 2√5 + 5√2 2x√3 - 11√2x 5a + 3√5a

  7. -14 - 10√5 (8 + 3√5 ) (2 – 2√5) (16) - 16√5 + 6 √5 - 6 (√25) 16 - 16 √5 + 6√5 - 6(5) 16 - 10√5 - 30

  8. 45 + 25√3 Your Turn! (3 + 2√3 ) (5 + 5√3) Simplify: (15) + 15√3 + 10 √3 +10 (√9) 15 + 15 √3 + 10√3 + 10(3) 15 - 25√3 + 30

  9. (√25) + √75 - 2 √75 - 2 (√225) 5 + √75 - 2√75 - 2(15) 5 - √75 - 30 -25 - √75 -25 - 5√3

  10. -33 - 21√2 2(√36) -10 √18 + 3 √18 - 15 (√9) 2(6) - 10√18 + 3√18 - 15(3) 12 - 7√18 - 45 -33 - 7√18

  11. 4√7 - 4√5 4√7 - 4√5 √7 - √5 4 √7 - √5 4√7 - 4√5 2√7 - 2√5 x √7 + √5 √7 - √5 √7 - √5 2 (√7)2 - (√5)2 7 - 5

  12. Addition and Subtraction of Radicals

  13. Warm - up

  14. 2x + 5x y + 10y 2x + 10y 3.) 2.) 1.) How do we combine like-terms = 7x = 11y = 2x + 10y

  15. radicand 4√7 √7 is radicand

  16. 2.) 4.) 9√3 + 2√3 4√5 - 3√5 √2 + √2 1.) 3.) CASE 1 √5 - √5 Addition and Subtraction of radicals with the same radicand = 2√2 = 0 = 1√5 = 11√3

  17. 2.) 4.) 4√7 + 3√5 9√1 + 2√9 √2 + √3 1.) 3.) CASE 2 √5 + √2 Addition of radicals with different radicand = √2 + √3 = √5 + √2 = 4√7 + 3√5 = 9√1 + 2√9

  18. 2 2 2 3 4 9 2 3 √8 + √18 1.) CASE 3 Addition of radicals with different radicand but can be simplified = 5√2 + 3√2 2√2

  19. 3 3 3 2 4 9 3 2 √27 + √12 2.) Your Turn! = 5√3 + 2√3 3√3

  20. 2√8 + 3√18 √7 + √3 2√2 + 7√2 1.) 2.) 3.) Practice: = √7 + √3 = 9√2 = 13√2

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