Simplify Radicals - PowerPoint Presentation

Slide1

Simplify Radicals

Lesson objectives

Teachers' notes

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 EducatorSlide2

12

96

Simplifying Radicals

Simplifying Radicals

54Slide3

To There

To There

From Here

From Here

How Do We Get

How Do We Get

54

6

3Slide4

I KNOW, I KNOW, 
pick me, pick me!!!

I KNOW, I KNOW, 
pick me, pick me!!!Slide5

Simplifying Radicals

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.Slide6

Simplifying Radicals

Simplifying Radicals

1

3

This is an example of an 
"exact form" fraction.

This is an example of an 
"approximate" fraction.

but it is really 


.333333333333333333333333333333333333333333333333333333333333...

.33Slide7

Simplifying Radicals

Simplifying Radicals

This is an example of an 
"exact form" radical.

This is an example of an 
"approximate" radical.

but

REALLY

7.3484692283495345 keeps 
going and going and going and going 
and going....

6

3

7.35Slide8

Simplifying Radicals

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

3Slide9

2

3

3

2

Simplifying Radicals

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 notationsSlide10

Simplifying Radicals

Simplifying Radicals

54

This is a "square" root so

let's find all the SQUARES

OR

...Rewrite and pull out the perfect squares

2

3

3

2

3Slide11

6

3

3

Simplifying Radicals

Simplifying Radicals

54

This is a "square" root so

let's find all the SQUARES

Multiply the remaining primes

under the square root sign.

And You're

Done!!

And You're

Done!! Slide12

Simplifying Radicals

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 = 144Slide13

22 = 4

32 = 9

42 = 1652 = 25

62 = 3672 = 49

82 = 64

92 = 81

102 = 100112 = 121122 = 144

Simplifying Radicals

Simplifying Radicals

108

Here Is

Another Method

Find the largest perfect square that will 
divide evenly into the radical.Slide14

Simplifying Radicals

Simplifying Radicals

108

Here Is

Another Method

Factor the two numbers to make the radical.

36

3Slide15

Simplifying Radicals

Simplifying Radicals

108

Here Is

Another Method

Rewrite and pull out the perfect squares.

36

3

62 = 36

6Slide16

Simplifying Radicals

Simplifying Radicals

252

Lastly...

The Calculator Method

Y=

2

2

5

X,T,

Θ,

n

÷

x2Slide17

Simplifying Radicals

Simplifying Radicals

252

Lastly...

The Calculator Method

2nd

GRAPH

The "y" side

is INSIDE

the radical sign

The "x" side

is OUTSIDE

the radical signSlide18

Simplifying Radicals

Simplifying Radicals

252

Lastly...

The Calculator Method

2nd

GRAPH

Choose the lowest

"y"

INTEGER

. There

should be no squares.

36

3

9

7

4

7

1

7

...no

...no

...no

...yesSlide19

7

6

Simplifying Radicals

Simplifying Radicals

Lastly.... 

The Calculator Method

Write the simplified version, "x" is outside 
and "y" is inside the radical sign

And You're

Done!!

And You're

Done!!

252Slide20

The Best Part.......

Choose What Is 
Easiest For You

The Best Part.......

Choose What Is 
Easiest For You

1st: Factor all primes

2nd: Factor perfect squares

3rd: Calculator methodSlide21

Practice Problems

Practice Problems

162

1152

432

9

x

700

-5Slide22

Practice Problems

Practice Problems

320x3

918m4n7

972x2yz5

3

xySlide23

Teachers' notes

Lesson objectives

Subject:

Topic:

Grade(s):

Prior knowledge:

Cross-curricular link(s):

Algebra 1

How to Simplify Radicals

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.

Sl

ide 11:

Touch next to Tigger on right side to have "And you're done" appear.

Sl

ide 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.

Sl

ide 19:

Touch next to Tigger on right side to have "And you're done" appear.

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