Download Prime Factorization

Review:
Review:
Prime
Prime Factorization
Factorization
48
60
72
Review:
Review:
Prime
Prime Factorization
Factorization
48
60
72
5
4 Simplifying Radicals
54
96
2
1
Simplifying
Simplifying Radicals
54
Before we start simplifying
radicals, we need to discuss
numbers in "exact form".
In general all integers, fractions, radicals and
the numbers e and π are considered to be exact
numbers and all numbers written in floating point
form (i.e. with a decimal point) are considered to
be approximate numbers.
Simplifying
Simplifying Radicals
54
This is a "square" root so
let's find all the SQUARES
Find all the "Prime Factors" of the number 54,
starting with the smallest prime.
2 3 3 3
Simplifying
Simplifying Radicals
54
This is a "square" root so
let's find all the SQUARES
Rewrite using square notations
2 3 3
2
Separate square root notations
3
2
23
Simplifying
Simplifying Radicals
54
This is a "square" root so
let's find all the SQUARES
OR...Rewrite and pull out the perfect squares
3
2 3 3
2
33
Simplifying
Simplifying Radicals
54
This is a "square" root so
let's find all the SQUARES
Multiply the remaining primes
under the square root sign.
3
3
6
And You're
Done!!
Go fish:
• pairs are laid down outside the hand
• singles are left in the hand
48
√2·2·2·2·3
√2 ·2 ·3
√2 ⋄ √2 ⋄ √3
2⋄2⋄√3
4√3
2
2
2
2
Go fish:
• pairs are laid down outside the hand
• singles are left in the hand
60
√2·2·3·5
√2 ·5·3
√2 ⋄ √5 ⋄ √3
2⋄√3⋄5
2√15
2
2
Go fish:
• pairs are laid down outside the hand
• singles are left in the hand
72
√2·2·2·3·3
√2 ·2·3
√2 ⋄ √2 ⋄ √3
2⋄3√2
6√2
2
2
2
2
√12
Go Fish
12
4 3
2 2 3
Simplifying
Simplifying Radicals
108
Here Is
Another Method
List all the perfect squares from 2 - 12.
2 =4
2
3 =9
2
4 = 16
2
5 = 25
2
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
2
11 = 121
122 = 144
Practice Problems
√28
√360
√50
Practice Problems
√175
√124
√112
Practice Problems
162
-5 700
1152
9 432
Practice Problems
320x
3
918m n
4 7
3xy 972x2yz5
Simplify the following radicals:
(Go Fish . . .)
23 25