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 Chabot Mathematics 7.3 Radical Products 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 MTH 55 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. 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. 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: MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 6 Bruce Mayer, PE Chabot College Mathematics Example Product Rule Multiply SOLUTION 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: 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) MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 9 Bruce Mayer, PE Chabot College Mathematics Example Product Rule Multiply SOLUTION 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 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 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. 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 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. 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. 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) MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 17 Bruce Mayer, PE Chabot College Mathematics All Done for Today Running Dinosaur 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. 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 Chabot Mathematics Appendix MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 20 Bruce Mayer, PE Chabot College Mathematics MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 21 Bruce Mayer, PE Chabot College Mathematics Graph y = |x| Make T-table MTH55_Lec-41_sec_7-3a_Radical_Product_Rule.ppt.ppt 22 Bruce Mayer, PE Chabot College Mathematics