Simplifying Radicals

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Simplifying Radicals
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Perfect Squares
Perfect Cubes
1
216
64
225
1
8
343
81
4
100
9
400
27
512
16
121
64
729
144
25
125
1000
625
169
36
196
49
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Simplify
4
4
2
6
8
This is a piece of cake!
12
4
Find the largest Perfect Square Factor
Simplify
LEAVE IN RADICAL FORM
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This time Prime Factor the radicand
Simplify
LEAVE IN RADICAL FORM
6
Simplify
7
and
Consider this
8
Simplify
9
Simplify
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Combining Radicals
To combine radicals combine the ______________
of __________ radicals
coefficients
like
11
Simplify each expression
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Simplify each expression Simplify each radical
first (largest perfect square) and then combine.
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Simplify each expression Simplify each radical
first (largest perfect square) and then combine.
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Multiplying Radicals
To multiply radicals multiply the _____________
and then multiply the _____________ .
Simplify the remaining radicals.
radicands
coefficients
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Multiply and then simplify
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Dividing Radicals
To divide radicals divide the____________, if
possible divide the __________, if
possible _________________ the denominator so
that no radical remains in the denominator
coefficients
radicands
Rationalize
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Rationalizing the denominator. This expression
can not be divided which leaves a radical in the
denominator. We do not leave radicals in the
denominator. So we need to rationalize by
multiplying the fraction by something so we can
eliminate the radical in the denominator. Look
back at slide 15
42 cannot be simplified, so we are finished.
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This can be divided, but this leaves a radical in
the denominator. We do not radicals in the
denominator. So we need to rationalize by
multiplying the fraction by something so we can
eliminate the radical in the denominator.
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This cannot be divided which leaves the radical
in the denominator. We do not leave radicals in
the denominator. So we need to rationalize by
multiplying the fraction by something so we can
eliminate the radical in the denominator.
Reduce the fraction.
Reduce the fraction.