Transcript Warm-Up
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
96
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 3 223
7 32 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