7.5 Solving Radical Equations

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7.5 Solving Radical Equations
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What is a Radical Expression?
yes

• A Radical Expression is an equation that has a
  variable in a radicand or has a variable with a
  rational exponent.

yes
no
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EXAMPLE Solving a Radical Equation
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Square both sides to get rid of the square root
(
)
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EXAMPLE
2
2
(
)
NO SOLUTION Since 16 doesnt plug in as a
solution.
Note You will get Extraneous Solutions from time
to time always do a quick check
Lets Double Check that this works
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Lets Try Some
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Lets Try Some
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SOLVING MORE COMPLEX EQUATIONS
because we are taking an even power (square
root) of both sides
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RADICAL EQUATIONS
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDES TO RECIPROCAL POWER
SOLVE FOR THE VARIABLE
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SOLVING MORE COMPLEX EQUATIONS
Raise each side to the 4th power. This will get
you integer powers much easier to work with!
Factor
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Lets Try Some . . . check for extraneous
solutions
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Lets Try Some . . . check for extraneous
solutions
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Can graphing calculators help?

• SURE!
• Input for Y1
• Input x-2 for Y2
• Graph
• Find the points of intersection

One Solution at (4, 2)
To see if this is extraneous or not, plug the x
value back into the equation. Does it work?