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Geometry
Lesson 0 – 9
Square Roots and
Simplifying Radicals
Objective:
Evaluate square roots and simplify radical expressions.
Product Property
Product property:
 For
b,
any two positive numbers a and
ab  a  b
43  4  3
20  4  5
Simplifying radicals
A radical expression (square root
expression) is simplified when the
following are met:
 No
perfect square factors
 No fractions inside the radical sign
 No radicals in the denominator
 Expression has only 1 radical sign
Simplify
45
Is there a perfect square that is a factor of 45?
If so break down the expression,
if not it is already simplified.
 9 5
3 5
Notice that 9*5 = 45
Use your calculator to check
45  6.708...
3 5  6.708...
Simplify
50
 25 2
5 2
Simplify
300
Simplifying may take more than one steps
And can be worked different ways.
 25 12
 5 12
 5 4 3
 5 2 3
 10 3
Can still break down sq. root of 12.
or
300  100 3
 10 3
Simplify
6  15
6  15
 2 3 3 5
3 2 5
 3 10
 90
OR
 9 10
 3 10
Simplify
82 4
 4 2 22
 2 2 4
 4 2 2
8 2
Quotient Property
Quotient Property:

For any positive numbers a and b,
a
a

b
b
Simplify
25
16
25

16
5

4
49
36
49

36
7

6
Simplify
2
3
2 


3
2 3

3
Is not simplified because of the radical
in the denominator.
You can do anything to a fraction as long as
you do it to the numerator and denominator.
3


3
3 3  9 3
Simplify
3
5
 5


 5


3 5

5
3
5 2

Simplify
5 2 


5 2 



3 5 2
5 2 5 2


15  3 2
25  2

Multiply by what’s with the radical,
Only switch the sign.
Do FOIL method in denominator
5  2 5  2 
25  5 2  5 2  4
25  2
15  3 2
23
Simplify
8
6 3
6  3 
6  3 
48  8 3

36  3
48  6 3

33
Simplify
3
Break down numbers the same.
Break down variables in to ‘squares’
Remember x * x = x2
5 6
20 x y z
 4 5 x
 2x
2
2
y z3
x y
4
y
5xy
 2 xy z
2 3
5xy
z
6
Simplify
5 4 7
18a b c
 9 2 a
4
 3a b c
2 2 3
a b
4
2ac
c
6
c
Homework
Pg. P20 1 – 20 all