Simplify and add radicals
- 2. War m up solutions
- 4. Review of the basics In the expression 64, is the radical sign and 64 is the radicand. 1. Find the square root: 64 8 2. Find the square root: − 100 -10
- 5. 3. Find the squar e ± 121 r oot: 11, -11 4. Find the square root: 441 21 25 5. Find the square root: − 81 5 − 9
- 6. W hat number s ar e perfect squar es? 1•1=1 2•2=4 3•3=9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...
- 7. 1. Simplify 147 Find a perfect square that goes into 147. 147 = 49g3 147 = 49 g 3 147 = 7 3
- 8. 2. Simplify 605 Find a perfect square that goes into 605. 121g5 121g 5 11 5
- 9. Simplify 72 A. 2 18 B. 3 8 C. 6 2 D. 36 2 .
- 10. Perfect Square Factor * Other Factor 18 = 9× 2 = 3 2 LEAVE IN RADICAL FORM 288 = 144 × 2 = 12 2 75 = 25 3 = 5 3 24 = 4× 6 = 2 6 72 = 36 × 2 = 6 2
- 11. 4. Simplify 49x 2 Find a perfect square that goes into 49. 49 g x 2 7x 5. Simplify 8x = 8 g x 25 25 2 2 g x 24 x 24 2 2gx 2 x 2 x12 2 x
- 12. Simplify 36 9x A.3x6 B.3x18 C.9x6 D. 9x18 Worksheet #5 try #1, 8, 12
- 13. Intermediate Simplification Cube roots!!!! Simplify: Simplify: Simplify: Is this possible?? 3 6 54n 9 563 3 −8 ? Find a perfect cube that goes Into 54….. How about 9 ×3 8 ×3 7 −2 ×−2 ×−2 3 27 ×3 2 ×3 n6 3 6 18 7 3 −8 = − 2 3 ×3 2 ×n 3 Don’t forget Worksheet #5 23 to use the Try #3, 10, 14 3n 2 proper index!
- 14. Answer s: 3. − 3 6 3 3 10. 2m 3 14. − 2ab 23 2b 2
- 15. Intermediate Simplification - 4 th roots Simplify: Simplify: Simplify: Is this possible?? 4 20 32n 4 −256 ? Find a perfect forth root −2 324v 4 6 that goes into 32….. How about −2 ×4 81 ×4 4 ×4 v 4 ×4 v 2 −4 ×−4 ×−4 ×−4 4 16 ×4 2 ×4 n 20 4 = 256 2 × 2 ×n 4 20 4 − 2 ×3 × 4 ×v4 44 v 2 Make a conclusion 54 −6 v 4 v 4 2 about 2n 2 negative WS #5 Don’t forget to use radicands. the proper index! Try 7, 13, 15
- 16. Answer s: 24 7. 2n 8 3 2 13. 3 5 x y 4 3 3 15. 2 xy 8 x y4
- 17. Intermediate Simplification - 5 th roots Simplify: Simplify: Simplify: Is this possible?? 5 20 6250n 5 13 5 −32 ? Find a perfect fifth root 3 1215v that goes into 6250….. How about 3 ×5 243 ×5 5 ×5 v10 ×5 v 3 −2 ×−2 ×−2 ×−2 ×−2 5 3125 ×5 2 ×5 n 20 10 5 −32 = −2 20 3 ×3 × 5 ×v 5 5 5 v 3 Make a 5 × 2 ×n 4 5 conclusion 25 3 about 45 9v 5v negative 5n 2 radicands WS #5 Don’t forget to use and indexes. the proper index! Try 9, 17
- 18. Answer s: 5 2 9. 2r 7 r 17. 2 xy 7 xy 6 ½ sheet simplify – Pick 10 – make sure you pick different indexes – self check at the back table – Homework check
- 19. Simplifying Radicals • ½ sheet simplify – Pick 10 – make sure you pick different indexes – • self check at the back table – • Homework check • Review #5
- 20. + To add or subtact radicals: combine the coefficients of like radicals(same index and same radicand)
- 21. Simplify each expression Use what you know: add or subtract coefficients of like terms 6 x + 5 x − 3x = 8 x 6 7 +5 7 −3 7 = 8 7 5 6 +3 7 + 4 7 −2 6 = 3 6+7 7
- 22. Simplify each radical first and then combine like radicals. 2 25 ×2 − 3 16 ×2 = 2 50 − 3 32 = 2 ×5 2 − 3 ×4 2 = 10 2 − 12 2 = −2 2
- 23. Simplify each radical first and then combine like radicals. 3 27 + 5 48 = 3 9 × + 5 16 × = 3 3 Simplify each radical 3 × 3 + 5 ×4 3 = 3 multiply 9 3 + 20 3 = Add like radicals (like terms) 29 3
- 24. Simplify each expression 6 5 +5 6 −3 6 = 3 24 + 7 54 = 2 8 − 7 32 = Adding Subtracting worksheet # 3 – multiples of 3
- 25. Intermediate Add/Subtract radical expressions GROUP 1 GROUP 2 4 80 + 2 20 − 3 45 5 6 − 3 24 + 150 =5 6 − 3 4 6 + 25 6 4 16 5 + 2 4 5 − 4 9 5 = 5 6 − 3 ×2 × 6 + 5 6 4 ×4 × 5 + 2 ×2 × 5 − 4 × × 5 3 =5 6 − 6 6 + 5 6 16 5 + 4 5 − 12 5 4 6 11 5
- 26. Intermediate Add/Subtract radical expressions GROUP 1 GROUP 2 4 80 + 2 20 − 3 45 5 6 − 3 24 + 150 =5 6 − 3 4 6 + 25 6 4 16 5 + 2 4 5 − 4 9 5 = 5 6 − 3 ×2 × 6 + 5 6 4 ×4 × 5 + 2 ×2 × 5 − 4 × × 5 3 =5 6 − 6 6 + 5 6 16 5 + 4 5 − 12 5 4 6 11 5