1. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics §7.3 Factor Radicals

2. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 2 Bruce Mayer, PE Chabot College Mathematics Review §  Any QUESTIONS About §7.3 → Multiply Radicals  Any QUESTIONS About HomeWork §7.3 → HW-32 7.3 MTH 55

3. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 3 Bruce Mayer, PE Chabot College Mathematics Product Rule for Radicals  For any real numbers and  That is, The product of two n th roots is the n th root of the product of the two radicands.

4. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 4 Bruce Mayer, PE Chabot College Mathematics Simplifying by Factoring  The number p is a perfect square if there exists a rational number q for which q 2 = p. We say that p is a perfect n th power if q n = p for some rational number q.  The product rule allows us to simplify whenever ab contains a factor that is a perfect n th power

5. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 5 Bruce Mayer, PE Chabot College Mathematics Simplify by Product Rule  Use The Product Rule in REVERSE to Facilitate the Simplification process Note that and must both be real numbers

6. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 6 Bruce Mayer, PE Chabot College Mathematics Simplify a Radical Expression with Index n by Factoring 1.Express the radicand as a product in which one factor is the largest perfect n th power possible. 2.Take the n th root of each factor 3.Simplification is complete when no radicand has a factor that is a perfect n th power.

7. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 7 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring (assume x > 0) a)b)  SOLUTION → Match INDICES a) b)

8. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 8 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring (assume x > 0) a)b)  SOLN a) Note That the INDEX is 3

9. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 9 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring (assume x > 0) a)b)  SOLN b) Note INDEX of 5

10. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 10 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring (assume x, y > 0) a)b)  SOLN a) Note INDEX of 2

11. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 11 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring (assume x, y > 0) a)b)  SOLN b) Note INDEX of 3

12. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 12 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  Simplify by factoring (assume w, z > 0)  SOLN: First perform Distribution Note that all INDICES are common at 5

13. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 13 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLN: Use Radical Product Rule  SOLN: Use Commutative Property of Multiplication

14. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 14 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLN: Exponent Product Rule  SOLN: Next use Exponent POWER rule to expose as many bases as possible to the Power of 5; the Radical Index

15. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 15 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLN: Power-to-Power Exponent Rule  SOLN: Next Radical Product Rule

16. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 16 Bruce Mayer, PE Chabot College Mathematics Example  Simplify  SOLN: Perform 5 th Root Operations  SOLN: Finally Factor GCF = wz 2 ANS

17. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 17 Bruce Mayer, PE Chabot College Mathematics WhiteBoard Work  Problems From §7.3 Exercise Set 76, 80, 82, 92, 98  Adult Cardiac Index = 2.8-3.4

18. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 18 Bruce Mayer, PE Chabot College Mathematics All Done for Today Exponent Rules are NOT Algebraic

19. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 19 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics Appendix –

20. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 20 Bruce Mayer, PE Chabot College Mathematics Graph y = |x|  Make T-table

21. BMayer@ChabotCollege.edu MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt 21 Bruce Mayer, PE Chabot College Mathematics