PRODUCT RULE: π π QUOTIENT RULE: π βπ₯ βπ¦ π π₯ π βπ₯ β βπ¦ = βπ₯π¦ π = β π¦ Example: Example: β10 β βπ₯ = β10π₯ β10 β2 =β 10 2 = β5 More directly, when determining a product or quotient of radicals and the indices (the small number in front of the radical) are the same then you can rewrite 2 radicals as 1 or 1 radical as 2. Simplify by rewriting the following using only one radical sign (i.e. rewriting 2 radicals as 1). 1. β3 β β12 3. β7π₯ β β2π¦ 2. β12 β3 3 4. β12π₯ 2 3 β4π₯ Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2). 144 25 5. β 6. β π₯6 121 M. Winking (Section 1-8) p. 17 Express each radical in simplified form. 8. β450π₯ 4 π¦ 5 7. β48 9. β72π₯ 5 π¦ 6 P 10. β300π₯ 12 N 11. β675π₯ 4 π¦ 11 12. ββ81π₯ 3 π¦ 8 O 3 13. β48π₯ 7 π¦ 3 O N 14. A 3 3 β81π₯10 π¦ 3 15. ββ27π₯ 5 N I K Use the letters and answers to match the answer to the riddle. Only some answers will be used. βWhat is an opinion without Ο?β _________ β9π₯π¦ 4 βπ₯ _________ 15π₯ 2 π¦ 2 β2π¦ _________ 10π₯ 6 β3 _________ 3 2π₯ 2 π¦ β6π₯ _________ 3 3π₯ 3 π¦ β3π₯ _________ _________ 6π₯ 2 π¦ 3 β2π₯ 15π₯ 2 π¦ 5 β3π¦ M. Winking (Section 1-8) p. 18 Express each radical in simplified form. 17. β18π5 β β6π4 16. β6π₯ β β12π₯ Simplify. Assume that all variable represent positive real numbers. 18. 5β3 + β2 β 2β3 + 4β2 19. 21. π¦β18 β 3β12π¦ 4 + 2β8π¦ 2 ο¨ 24. 2 10 3 6 ο« 2 5 ο 24 ο© 108 ο« 5 12 ο 4 44 23. 5 18 x 4 ο 3x 8 x 2 ο x 2 2 22. π₯ β32π₯ 2 + 2 β18π₯ 4 25. 2x ο¨ 6x ο« 3 x 20. 2 150 ο« 18 ο« 3 8 ο 24 ο© 26. 3 6a ο¨ 4a ο« 2 15a 2 ο© p. 101 M. Winking (Section 1-8) p. 19 Simplify. Assume that all variable represent positive real numbers and rationalize all denominators. 18. 3 β5 16 21. β27 19. 6 β3 22. 20. 12 ο« 8 3 ο 2 27 2 3β2 β6 23. β2(β12ββ3) β3 M. Winking (Section 1-8) p. 20
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