11.2 multiplying rads notes.notebook
April 02, 2013
11.2 Multiply Radicals
1) Lesson objective to simplify radicals in exact form.
2) Introducing three methods, prime factorization, largest
square, and the calculator method.
Lesson objectives
Apr 2­7:50 AM
Nov 4­10:26 AM
Simplifying
Simplifying Radicals
How Do We Get
From Here
96
2
1
Teachers' notes
54
May 9­9:39 AM
To There
54
3 6
May 9­9:39 AM
1
11.2 multiplying rads notes.notebook
I KNOW, I KNOW,
pick me, pick me!!!
me!!!
April 02, 2013
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.
May 9­9:39 AM
May 9­9:39 AM
Simplifying
Simplifying Radicals
Simplifying
Simplifying Radicals
This is an example of an
"exact form" fraction.
1
3
This is an example of an
"exact form" radical.
3 6
This is an example of an
"approximate" fraction.
.33
This is an example of an
"approximate" radical.
7.35
but it is really .3333333333333333333333333333333
33333333333333333333333333333...
May 9­9:39 AM
but REALLY 7.3484692283495345 keeps
going and going and going and going
and going....
May 9­9:39 AM
2
11.2 multiplying rads notes.notebook
April 02, 2013
Simplifying
Simplifying Radicals
Simplifying
Simplifying Radicals
54
This is a "square" root so
let's find all the SQUARES
54
This is a "square" root so
let's find all the SQUARES
Rewrite using square notations
2 3 32
Find all the "Prime Factors" of the number 54,
starting with the smallest prime.
Separate square root notations
32 2 3
2 3 3 3
May 9­9:39 AM
May 9­9:39 AM
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
Apr 2­1:23 PM
2 3 32
May 9­9:39 AM
3
11.2 multiplying rads notes.notebook
Simplifying
Simplifying Radicals
This is a "square" root so
let's find all the SQUARES
54
Multiply the remaining primes
under the square root sign.
3
6
And
And You're
Done!!
May 9­9:39 AM
April 02, 2013
Simplifying
Simplifying Radicals
108
Here Is
Another Method
List all the perfect squares from 2 - 12.
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
May 9­9:39 AM
Simplifying
Simplifying Radicals
Simplifying
Simplifying Radicals
108
Here Is
Another Method
Find the largest perfect square that will
divide evenly into the radical.
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
May 9­9:39 AM
108
Here Is
Another Method
Factor the two numbers to make the radical.
3 36
102 = 100
112 = 121
122 = 144
May 9­9:39 AM
4
11.2 multiplying rads notes.notebook
Simplifying
Simplifying Radicals
108
Here Is
Another Method
Rewrite and pull out the perfect squares.
62 = 36
6
3 36
May 9­9:39 AM
Practice Problems
­5 700
162
1152
9x 432
April 02, 2013
The Best Part.......
Choose What Is
Easiest For You
1st: Factor all primes
2nd: Factor perfect squares
May 9­9:39 AM
Practice Problems
320x3
918m4n7
3xy 972x2yz5
May 9­9:39 AM
May 9­9:39 AM
5