W A T K I N S - J O H N S O N C O M P A N Y Semiconductor Equipment Group

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Chabot Mathematics
7.3 FactorRadicals
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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Review

• Any QUESTIONS About
• 7.3 ? Multiply Radicals
• Any QUESTIONS About HomeWork
• 7.3 ? HW-32

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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.

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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

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Simplify by Product Rule

• Use The Product Rule in REVERSE to Facilitate the
  Simplification process

• Note that and must both be real numbers

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Simplify a Radical Expression with Index n by
Factoring

1. Express the radicand as a product in which one
   factor is the largest perfect nth power possible.
2. Take the nth root of each factor
3. Simplification is complete when no radicand has a
   factor that is a perfect nth power.

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Example ? Simplify by Factoring

• Simplify by factoring (assume x gt 0)
• a) b)

• SOLUTION ? Match INDICES
• a) b)

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Example ? Simplify by Factoring

• Simplify by factoring (assume x gt 0)
• a) b)

• SOLN a)NoteThat theINDEXis 3

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Example ? Simplify by Factoring

• Simplify by factoring (assume x gt 0)
• a) b)

• SOLN b) Note INDEX of 5

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Example ? Simplify by Factoring

• Simplify by factoring (assume x, y gt 0)
• a) b)

• SOLN a) Note INDEX of 2

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Example ? Simplify by Factoring

• Simplify by factoring (assume x, y gt 0)
• a) b)

• SOLN b) Note INDEX of 3

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Example ? Simplify

• Simplify by factoring (assume w, z gt 0)

• SOLN First perform Distribution
• Note that all INDICES are common at 5

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Example ? Simplify

• SOLN Use Radical Product Rule

• SOLN Use Commutative Property of Multiplication

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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

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Example ? Simplify

• SOLN Power-to-Power Exponent Rule

• SOLN Next Radical Product Rule

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Example ? Simplify

• SOLN Perform 5th Root Operations

• SOLN Finally Factor GCF wz2

ANS
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WhiteBoard Work

• Problems From 7.3 Exercise Set
• 76, 80, 82, 92, 98

• AdultCardiacIndex 2.8-3.4

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All Done for Today
ExponentRules are NOTAlgebraic
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Chabot Mathematics
Appendix
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu

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Graph y x

• Make T-table

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