Download PPadua-Douglas,E. CNM 2012-01-09 9812



January 10, 2012
At the end of today, you will be able to simplify
radical expressions by using multiplication and
addition.
Warm-up: Simplify.
1.
2
 x  4x  4
3.
5. t  3t  20
2
t 2
3
8a3b9
4. (32)
16a2b2
5
2.



3
5
QUIZ 5.2 TODAY!
HW 5.6: Pg. 254
#15-23, 35-38 all
Correct HW 5.7 #1-20
1. 6 3
2. 5 8
3. 3 122 or
4. s5 s4
1
5. 512
1
6. 37 3
3
7. 15 4
 12 
3
2
8. 6
9.
10.
11.
12.
13.
14.
1
3
1
3
2
3
1
2 3
x y or (6xy )
2
3
1/3
1/2
64
81

15. 729
16. 8/27
17. c3
18. m2
3
19. q 2
20. p
p
1
5
Properties of Radicals
• Product Property:
Example:
8 4 2
• Quotient 
Property:
n

Example:
3

ab  n a  n b
n
a na
n
b
b
27 3 27
 3
8
8
Simplifying Radicals that aren’t perfect
“Ms. PD has another way to
simplify radicals using prime
numbers, ask her!”
A prime number is a
natural number greater
than 1 that is only divisible
by 1 and itself.
Example 1: Simplify:
Drake: “Think of
two numbers, one
of them a square#,
multiplied to give
you 40.”
1. Rewrite as two
radicals (one of
them a square)



40
4  10
2  10
 2 10


More simplifying radicals that aren’t
perfect…
1a.  27
 3 3
2.
16p q
8 7
 4 p4
q3 q
3.
3 4

40a b
 2ab 10a
2
b.
C.
48
4 3
8
2
 4p q
7
2


3
16
2 3 2
For variables, divide the
power by the index. If
there is a remainder, it
stays in the radical sign.
Like Radical Expressions
You can add and subtract radicals if they have the
same number under the radical.
For example: 3 5  6 5  5  10 5
Simplify:
First, simplify
the radicals
to get like
radicals. 

2 12  2 27  2 48
2 2 3 2 3 3  4 3
 4 3 6 3 4 3
2 3