Notes
Slide Show
Outline
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Radicals
and
Rational Exponents
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Simplifying Radicals
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Types of Roots
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Types of Roots:  Examples
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"For any real number a"
  • For any real number a, and any integer n  (n > 1),
  • If n is even,
  • then nÖan  =  ça ê
  • Example:
  •    2Ö42     = ê4 ï= 4
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Multiply Radicals
  •      nÖa  ·  nÖb  =  nÖab    (when a and b are real numbers)


  • Example:
  • (1) Ö2x4  ·Ö8y2  =  Ö16x4y2  = Ö 42(x2)2y2 = 4x2y
  • (2)  3Öx9  ·  3Ö27 = 3Ö27x9  =  3Ö33(x3)3 = 3x3
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"Examples:"
  •      Examples:
  • (1)


  • (2)
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Add and Subtract Radicals
  •     anÖx   ±  bnÖx  =  (a ± b) nÖx
  • Example:
  • (1)  Ö8  +  Ö32  =  Ö4  Ö2  +  Ö16  Ö2
  •                              =  2 Ö2 +  4 Ö2                   =  (2 + 4)Ö2
  •            =  6 Ö2
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"Add and Subtract Radicals"
  • Add and Subtract Radicals
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Rationalize the Denominator
  • Example:
  • To rationalize the denominator of       , for example, multiply by      , which equals one.
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Laws of Rational Exponents
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"Examples:"
  • Examples:
  • (1)
  • (2)
  • (3)
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Guidelines for Simplifying Radicals and Exponents
  • no radicals in denominator
  • no fractional exponents in denominator
  • no fractions under radical sign (radicand)
  • no reducible exponents
  • no reducible root indexes
  • no negative exponents
  • no complex fractions