Simplify Radicals
1) Lesson objective to simplify radicals in exact form.
2) Introducing three methods, prime factorization, largest
square, and the calculator method.
Sue Blakely
Smart Exemplary Educator
Lesson objectives
Teachers' notes
Simplifying
Simplifying Radicals
Radicals
54
How Do We Get
From Here
To There
There
54
3 6
I KNOW, I KNOW, pick me,
pick me!!!
Simplifying
Simplifying Radicals
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
Radicals
This is an example of an "exact form"
fraction.
1
3
This is an example of an "approximate"
fraction.
.33
but it is really
.3333333333333333333333333333333
33333333333333333333333333333...
Simplifying
Simplifying Radicals
Radicals
This is an example of an "exact form"
radical.
3
6
This is an example of an "approximate"
radical.
7.35
but REALLY 7.3484692283495345 keeps
going and going and going and going and
going....
Simplifying
Simplifying Radicals
Radicals
This is a "square" root so
let's find all the SQUARES
54
Find all the "Prime Factors" of the number 54, starting with the
smallest prime.
2
3
3
3
Simplifying
Simplifying Radicals
Radicals
54
This is a "square" root so
let's find all the SQUARES
Rewrite using square notations
3
2
3
2
Separate square root notations
3
2
2 3
Simplifying
Simplifying Radicals
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
Simplifying
Simplifying Radicals
Radicals
54
This is a "square" root so
let's find all the SQUARES
Multiply the remaining primes
under the square root sign.
33
6
And You're
Done!!
Simplifying
Simplifying Radicals
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
Simplifying
Simplifying Radicals
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
102 = 100
112 = 121
122 = 144
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
Factor the two numbers to make the radical.
3
36
Simplifying
Simplifying Radicals
Radicals
108
Here Is
Another Method
Rewrite and pull out the perfect squares.
62 = 36
6
3
36
Simplifying
Simplifying Radicals
Radicals
Lastly...
The Calculator Method
252
Y=
2
÷
5
X,T,Θ,n
2
x2
Simplifying
Simplifying Radicals
Radicals
252
2nd
Lastly...
The Calculator Method
GRAPH
The "x" side
is OUTSIDE
the radical sign
The "y" side
is INSIDE
the radical sign
Simplifying
Simplifying Radicals
Radicals
252
2nd
GRAPH
Choose the lowest
"y" INTEGER. There
should be no squares.
Lastly...
The Calculator Method
...no
9 7 ...no
4 7 ...no
36 3
1 7 ...yes
Simplifying
Simplifying Radicals
Radicals
252
Lastly....
The Calculator Method
Write the simplified version, "x" is outside and "y" is inside the
radical sign
6
7
And You're
Done!!
The Best Part.......
Choose What Is Easiest For
You
1st: Factor all primes
2nd: Factor perfect squares
3rd: Calculator method
Practice Problems
162
-5
700
1152
9x
432
Practice Problems
320x3
918m4n7
3xy
972x2yz5
Subject:
Topic:
Algebra 1
How to Simplify Radicals
Grade(s):
Prior knowledge:
Cross-curricular link(s):
9-12
square roots, simplifying expressions,
prime factorization
Lesson notes:
Slide 10: Touch the last 3 squared to have it fade away. Touch next to the radical sign to
have a 3 appear before the radical sign.
Slide 11: Touch next to Tigger on right side to have "And you're done" appear.
Slide 15: Touch the yellow box to have it fade away. Touch next to the radical sign to
have a 6 appear before the radical sign.
Slide 19: Touch next to Tigger on right side to have "And you're done" appear.
animations from www.gifanimations.com, www.animatedgif.net (touch text to see copyright information)
Lesson objectives
Teachers' notes
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