Radicals are in simplest form when:

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Radicals are in simplest form when

• No factor of the radicand is a perfect square
  other than 1.
• The radicand contains no fractions
• No radical appears in the denominator of a
  fraction

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Perfect Squares
64
225
1
81
256
4
100
289
9
121
16
324
144
25
400
169
36
49
196
625
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Multiplication property of square roots

• Division property of square roots

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Simplify
2
4
5
This is a piece of cake!
10
12
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To Simplify Radicals you must make sure that you
do not leave any perfect square factors under the
radical sign.Think of the factors of the
radicand that are perfect squares.
Perfect Square Factor Other Factor

LEAVE IN RADICAL FORM

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Perfect Square Factor Other Factor
Simplify






LEAVE IN RADICAL FORM




7
Perfect Square Factor Other Factor
Simplify






LEAVE IN RADICAL FORM




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• If you cannot think of any factors that are
  perfect squares prime factor the radicand to
  see if you have any repeated factors
• EX

• 20
• 10
• 2 5

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You can simplify radicals that have variables TOO!





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Radicals are in simplest form when

• No factor of the radicand is a perfect square
  other than 1.
• The radicand contains no fractions
• No radical appears in the denominator of a
  fraction

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Multiply Square Roots

• REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS

OR
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Multiply Square Roots

• To multiply square roots
• you multiply the radicands together then simplify

EX



4
Simplify

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Try These



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Lets try some more
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Multiply Square Roots

• Multiply the coefficients
• Multiply the radicands
• Simplify the radical.

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Multiply Simplify Practice
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Homework Practice
1.
2.
3.
4.
5.
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Radicals are in simplest form when

• No factor of the radicand is a perfect square
  other than 1.
• The radicand contains no fractions
• No radical appears in the denominator of a
  fraction

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• Division property of square roots

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To simplify a radicand that contains a fraction
first put a separate radical in the numerator
and denominator
Then simplify
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Try These
Simplify
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If we have a radical left in the denominator
then we must rationalize the denominator
Since we cannot leave a radical in the
denominator we must multiply both the numerator
and the denominator by this radical to rationalize





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• Simplify
• Hint you will need to rationalize the
  denominator
• A.
• B. 4 
• C.
• D. 16 

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Simplify Radicals

• 1)
• 2)
• 3)
• 4)

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• 5)
• 6)
• 7)
• 8)

Simplify some more
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Review writing in simplest radical form

• 1)
• 2)
• 3)
• 4)

5) 6)
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Review writing in simplest radical form

• 7)
• 8)
• 9)

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• Which of the following is not a condition
• of a radical expression in simplest form? 
• A. No radicals appear in the numerator of a
  fraction. 
• B. No radicands have perfect square factors
  other than 1. 
• C. No radicals appear in the denominator
  of a fraction. 
• D. No radicands contain fractions.

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Adding and subtracting radical expressions

• You can only add or subtract radicals together if
  they are like radicals the radicands MUST be
  the same