8'4 Rationalizing Denominators

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8.4 Rationalizing Denominators
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Rationalizing Denominators

• Unacceptable Forms
• Radicands cannot be fractions
• Cannot have radicals in denominators
• Most radicals are IRRATIONAL numbers
• Our Goal Make them RATIONAL, that is PERFECT
  SQUARES or PERFECT CUBES

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Rationalizing Denominators
Make the denominator a PERFECT SQUARE
Must multiply the numerator by the same number
Multiply
Simplify
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Rationalizing Cube Roots
Have to make the denominator a
PERFECT CUBE
PERFECT CUBE
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Rationalizing with CONJUGATES
Lets take two problems that look very similar.
F O I L and the answer still has radicals in it!
F O I L and the radicals drop out of the answer.
The numbers in the right-hand problem are called
CONJUGATES.
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Conjugate Rationalization
Determine the conjugate same numbers as original
denominator with opposite sign.
Just do the F L of F O I L
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Determine the conjugate same numbers as original
denominator with opposite sign.
Use F O I L in the numerator and just F L in the
denominator
Simplify
or
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Determine the conjugate same numbers as original
denominator with opposite sign.
Use F O I L in the numerator And just F L in the
denominator
Simplify
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8.4 Rationalizing Denominators

• End of slide presentation!