1. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics §7.3 Radical Products

2. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 2 Bruce Mayer, PE Chabot College Mathematics Review §  Any QUESTIONS About §7.2 → Rational Exponents  Any QUESTIONS About HomeWork §7.2 → HW-25 7.2 MTH 55

3. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 3 Bruce Mayer, PE Chabot College Mathematics Multiplying Radical Expressions  Note That:  This example suggests the following.

4. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 4 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.

5. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 5 Bruce Mayer, PE Chabot College Mathematics Derive Product Rule for Rads  Rational exponents can be used to derive the Product Rule for Radicals:

6. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 6 Bruce Mayer, PE Chabot College Mathematics Example  Product Rule  Multiply  SOLUTION

7. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 7 Bruce Mayer, PE Chabot College Mathematics Caveat Product Rule  CAUTION  The product rule for radicals applies only when radicals have the SAME index:

8. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 8 Bruce Mayer, PE Chabot College Mathematics Example  Product Rule  Find the product and write the answer in simplest form. Assume all variables represent nonnegative values. a)b)  SOLN a)b)

9. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 9 Bruce Mayer, PE Chabot College Mathematics Example  Product Rule  Multiply  SOLUTION

10. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 10 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

11. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 11 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

12. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 12 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.

13. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 13 Bruce Mayer, PE Chabot College Mathematics Nix Negative Radicands  It is often safe to assume that a radicand does not represent a negative number when the radicand is raised to an even power  To Clarify the Essence of Radical Simplification We will make this assumption i.e., do NOT Need AbsVal bars

14. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 14 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify by factoring  SOLUTION 100 is the largest perfect- square factor of 300.

15. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 15 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  SOLUTION: 27s 3 is the largest perfect third-power factor.

16. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 16 Bruce Mayer, PE Chabot College Mathematics WhiteBoard Work  Problems From §7.3 Exercise Set 14, 18, 20, 32, 38, 56, 96  Estimating Dinosaur Speed (h ≡ hip hgt)  v = [gh(SL/1.8h) 2.56 ] 0.5 (Thulborn)  v = 0.25*g 0.5 *SL 1.67 *h −1.17 (Alexander)

17. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 17 Bruce Mayer, PE Chabot College Mathematics All Done for Today Running Dinosaur

18. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 18 Bruce Mayer, PE Chabot College Mathematics Example  Simplify by Factoring  Simplify  SOLUTION Cannot be simplified further.

19. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.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-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 20 Bruce Mayer, PE Chabot College Mathematics

21. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 21 Bruce Mayer, PE Chabot College Mathematics Graph y = |x|  Make T-table

22. BMayer@ChabotCollege.edu MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 22 Bruce Mayer, PE Chabot College Mathematics