Notes
Slide Show
Outline
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Equations with Radicals
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Steps to Solving Equations
with Radicals
  • Isolate the radical
  • Square both sides of the equation
  •    (or raise to appropriate power)
  • Solve for the variable
  • Check all solutions.  If the answer(s) does not work, the equation may not have a real number solution.
  •    Note: You can also use the properties of
  •               radicals to solve equations
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Radical Equations EXAMPLE 1
  • Example 1:
  • use properties of radicals
  •          isolate the variable
  •                                                          distributive property


  • rationalize the denominator


  • the conjugate of               is


  • when the two binomials in the
  •                                                 denominator are multiplied out,
  • the two center terms cancel each other


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EXAMPLE 1    page 2
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Radical Equations EXAMPLE 2
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Radical Equations EXAMPLE 3
  • Example 3:


  • isolate the radical
  • square both sides
  • solve for the variable



  • Check the solution in the original equation:



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Radical Equations EXAMPLE 4
  •  Example 4:


  •        isolate one of the radicals
  •            square both sides



  •            isolate the radical



  •            square both sides


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EXAMPLE 4    page 2
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Equations with Radicals:  EXERCISES
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Equations with Radicals:  EXERCISES 2
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Equations with Radicals:  EXERCISES 3