Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics §7.3 Factor Radicals Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

7.3 Review § Any QUESTIONS About Any QUESTIONS About HomeWork MTH 55 Review § Any QUESTIONS About §7.3 → Multiply Radicals Any QUESTIONS About HomeWork §7.3 → HW-26

Product Rule for Radicals For any real numbers and That is, The product of two nth roots is the nth root of the product of the two radicands.

Simplifying by Factoring The number p is a perfect square if there exists a rational number q for which q2 = p. We say that p is a perfect nth power if qn = p for some rational number q. The product rule allows us to simplify whenever ab contains a factor that is a perfect nth power

Simplify by Product Rule Use The Product Rule in REVERSE to Facilitate the Simplification process Note that and must both be real numbers

Simplify a Radical Expression with Index n by Factoring Express the radicand as a product in which one factor is the largest perfect nth power possible. Take the nth root of each factor Simplification is complete when no radicand has a factor that is a perfect nth power.

Example  Simplify by Factoring Simplify by factoring (assume x > 0) a) b) SOLUTION → Match INDICES a) b)

Example  Simplify by Factoring Simplify by factoring (assume x > 0) a) b) SOLN a) Note That the INDEX is 3

Example  Simplify by Factoring Simplify by factoring (assume x > 0) a) b) SOLN b) Note INDEX of 5

Example  Simplify by Factoring Simplify by factoring (assume x, y > 0) a) b) SOLN a) Note INDEX of 2

Example  Simplify by Factoring Simplify by factoring (assume x, y > 0) a) b) SOLN b) Note INDEX of 3

Example  Simplify Simplify by factoring (assume w, z > 0) SOLN: First perform Distribution Note that all INDICES are common at 5

Example  Simplify SOLN: Use Radical Product Rule SOLN: Use Commutative Property of Multiplication

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

Example  Simplify SOLN: Power-to-Power Exponent Rule SOLN: Next Radical Product Rule

Example  Simplify SOLN: Perform 5th Root Operations SOLN: Finally Factor GCF = wz2 ANS

WhiteBoard Work Problems From §7.3 Exercise Set 76, 80, 82, 92, 98 Adult Cardiac Index = 2.8-3.4

Exponent Rules are NOT Algebraic All Done for Today Exponent Rules are NOT Algebraic

Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Mathematics Appendix Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu –

Graph y = |x| Make T-table