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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Chabot Mathematics. §7.3 Factor Radicals. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. MTH 55. 7.3. Review §. Any QUESTIONS About §7.3 → Multiply Radicals Any QUESTIONS About HomeWork §7.3 → HW-32. Product Rule for Radicals.

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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  1. Chabot Mathematics §7.3 FactorRadicals Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. MTH 55 7.3 Review § • Any QUESTIONS About • §7.3 → Multiply Radicals • Any QUESTIONS About HomeWork • §7.3 → HW-32

  3. 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.

  4. 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

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

  6. 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.

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

  8. Example  Simplify by Factoring • Simplify by factoring (assume x > 0) a) b) • SOLN a)NoteThat theINDEXis 3

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

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

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

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

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

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

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

  17. WhiteBoard Work • Problems From §7.3 Exercise Set • 76, 80, 82, 92, 98 • AdultCardiacIndex =2.8-3.4

  18. All Done for Today ExponentRules are NOTAlgebraic

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

  20. Graph y = |x| • Make T-table

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