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G1-2 Simplifying Radicals
Hauen laguntzarekin: Cason
(Jatorrizko autorea: Pappal)
There are four types of radicals:
There are four types of radicals:
√4
Radicals with a perfect square
There are four types of radicals:
√4
√12
Radicals with a perfect square
Radicals that have a factor that is
a perfect square
There are four types of radicals:
√4
√12
√13
Radicals with a perfect square
Radicals that have a factor that is
Radicals that do not have a factor that is
a perfect square
a perfect square
There are four types of radicals:
√4
√12
√13
√-1
Radicals with a perfect square
Radicals that have a factor that is
Radicals that do not have a factor that is
Radicals that have a negative number
a perfect square
a perfect square
Match
√4
?
√-1
?
Radicals that have a negative number
Radicals with a perfect square
Radicals that have a perfect square are easy:
Radicals that have a perfect square are easy:
√4
Radicals that have a perfect square are easy:
√4
Just solve for the square root
of the number
Radicals that have a perfect square are easy:
√4 = 2
Just solve for the square root
of the number

Find the answer

√9 = 3

Find the answer

√9 = 3
√100 = 10

Find the answer

√9 = 3
√100 = 10
√25 = 5
Radicals that have a factor of a perfect square
are more difficult
Radicals that have a factor of a perfect square
√12
are more difficult
Radicals that have a factor of a perfect square
√12
are more difficult
First find the set of factors that has
the perfect square
Radicals that have a factor of a perfect square
2•6 = 12
√12
are more difficult
Neither 2 nor 6 is a perfect square
First find the set of factors that has
the perfect square
Radicals that have a factor of a perfect square
3•4 = 12
2•6 = 12
√12
are more difficult
Four is a perfect square
First find the set of factors that has
the perfect square
Radicals that have a factor of a perfect square
3•4 = 12
√12 = √4•√3
are more difficult
First find the set of factors that has
Then split the number into
the perfect square
those factors
Radicals that have a factor of a perfect square
√12 = √4•√3
are more difficult
First find the set of factors that has
Then split the number into
Finally, simplify the radical
the perfect square
those factors
with the perfect square
Radicals that have a factor of a perfect square
√4 = 2
√12 = √4•√3
are more difficult
First find the set of factors that has
Then split the number into
Finally, simplify the radical
the perfect square
those factors
with the perfect square
Radicals that have a factor of a perfect square
√12 = √4•√3 = 2√3
are more difficult
First find the set of factors that has
Then split the number into
Finally, simplify the radical
the perfect square
those factors
with the perfect square
Which set of factors has the perfect square

2•10

4•5

√20
Which set of factors has the perfect square
So we split the number into 4•
√20
Which set of factors has the perfect square
√20 = √4 • √5
=
√4 is a perfect square - Simplify it.
√5
Radicals that don't have a perfect square factor:
Radicals that don't have a perfect square factor:
√21
Radicals that don't have a perfect square factor:
√21
are easy because there isn't
any way to simpify
Radicals that don't have a perfect square factor:
√21
the only set of factors for 21
are easy because there isn't
(other than 1•21)
are 3 and 7
any way to simpify
Radicals that don't have a perfect square factor:
3•7
√21
the only set of factors for 21
are easy because there isn't
(other than 1•21)
are 3 and 7
any way to simpify
Radicals that don't have a perfect square factor:
3•7
√21
Since neither 3 nor 7 are perfect squares
the only set of factors for 21
are easy because there isn't
(other than 1•21)
are 3 and 7
any way to simpify
Radicals that don't have a perfect square factor:
3•7
√21
Since neither 3 nor 7 are perfect squares
there isn't any way to simplify
the only set of factors for 21
are easy because there isn't
(other than 1•21)
are 3 and 7
any way to simpify
Radicals that don't have a perfect square factor:
3•7
√21 = √21
Since neither 3 nor 7 are perfect squares
So it just stays √21
there isn't any way to simplify
the only set of factors for 21
are easy because there isn't
(other than 1•21)
are 3 and 7
any way to simpify
Solve
√26 = √26
Solve
√26 = √26
√51 = √51
Solve
√26 = √26
√51 = √51
√6 = √6
Which of these number is a perfect square?

3

64

99

149

Which of these number is a perfect square?

5

47

49

125

The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.  They keep going; however, these are the main ones we use. 
What perfect square is inside 99?  

The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.  They keep going; however, these are the main ones we use. 
What perfect square is inside 8?  

The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.  They keep going; however, these are the main ones we use. 
What perfect square is inside 125?  

The first 15 perfect squares are as follows:1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.  They keep going; however, these are the main ones we use. 
What perfect square is inside 24?  

√20 = √4 • √5 = 2√5
Solve
√20 = √4 • √5 = 2√5
√100 = 10
Solve
√20 = √4 • √5 = 2√5
√100 = 10
√33 = √
Solve
√20 = √4 • √5 = 2√5
√100 = 10
√33 = √33
√8 = 2√2
Solve
Simplify the following:
√125    =
√60
√27   =
√68    =
=
Negative radicals are not real as no number multiplied 
by itself can be negative.
There are four types of radicals:
√12
√13
√4
In summary...
√-1
=2
= 2√3
=√13
not real
Radicals that do not have a factor that is
Radicals that have a negative number
Radicals that have a factor that is
Radicals with a perfect square
a perfect square
a perfect square
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