April 22, 2015
Lesson 10.5
Rationalizing Numerators
and Denominators of Radical Expressions
Rules for rationalizing denominators of fractions.
A radical expression is in simplest form if
1) The radicand has no factor raised to a power
greater than or equal to the index.
2) There are neither radicals in the denominator
of a fraction nor radicals that are fractions.
3) All possible sum, differences, products and
quotients have been found.
Consider
We multiply an expression by a "Clever Form of
One" to rationalize its denominator if necessary.
Consider
and
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April 22, 2015
Rationalize the denominator.
This is an example of the property that
for all positive real numbers.
The same strategy works for higher indeces.
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What do we call the expressions
To rationalize the denominator of
?
we must
multiply by a clever form of one using the conjugate
of the denominator of the fraction.
Rationalize the denominator of each.
Reduce the radical expression.
We are only able to reduce when the numerator
and denominator have a common factor!
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