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Radical Expressions
Before we learn about radicals…
When a number is raised to the second
squared
power, the number is called _________.
Perfect square of the
 The result is the ________
original number.

Root
The original number is the _________
of
the result.
Perfect Squares
root
Perfect squares are numbers whose _______
__________ is a whole number.
 List the first 10 perfect squares:

12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
Can we find Perfect Squares
beyond 10?
112=
121
122=
144
132=
169
142=
196
152=
225
Let’s practice
16 
4
25 
5
81 
9
64 
8
49 
7
144 
12
169 
13
Square roots

What about
50 ?
Perfect
Square

50 is not a _______ _______.

so we will simplify…
 The
Square roots

One method is to
Look for twins…
(must be prime)
5
50
5
10
2
50
=
5 2
other method is on
simple problems to Look for
parts of roots…
50
=
50
=
25  2
5 2
Square roots

2) Simplify…
or
54
2
54
96
54
3
27
3 9
3
54
Same answer either method!!!!!!!
=
3 6
Square roots

3) Simplify…
2
48
48
48
2
or
16  3
24
2
12
2
6
3
48  2  2 3
48  4 3
Question!
What if you don’t have
‘twins?’
33 
3
33
11
or
11  3
Two numbers
with no perfect
square
Then the answer is …..
No twins to circle
33
Your turn!
80 
4 5
120 
2 30
27 
3 3
56 
2 14
Adding or subtracting radicals
To add or subtract radicals…
radical can be
 Check whether either ______
simplified
_______
radicals
 Check whether any of the ________
match
radical like a _______
variable and
 Treat the _______
add or subtract.
Simplify
Ex. 1
6 7 4 7
 10 7
Treat it like a variable.
Simplify
Ex. 2
3 5 5
4 5
Treat it like a variable.
Simplify
Ex. 3
7 3  12
 7 3  2 23
7 32 3
9 3
Treat it like a variable.
Simplify
Ex. 4
7 45  2 5
 7 3 3 5  2 5
 21 5  2 5
 19 5
Treat it like a variable.
Simplify
Ex. 5
5 2 4 3
not possible
Treat it like a variable.
Multiplying & Dividing
Radical Expressions
Multiplying radical expressions
radicals
multiplying __________,
multiply
_________
what is inside
multiply
(_________
what is outside).
 When
a  b  ab
Ex 1
Simplify
7  11
 77
Ex 2
Simplify
7 2 4 3
 28 6
Ex 3
Simplify
7 2  3 10
 21 20
Dividing radical expressions
radicals
multiplying __________,
divide
_________
what is inside
divide
(_________
what is outside).
 When
a
a

b
b
Ex 4
Simplify
26
2
26

2
 13
Ex 5
Simplify
27
3
27

3
 9
=3
Ex 6
Simplify
6 14
2 2
6 14

2 2
3 7