Simplify Radicals

Lesson objectives Teachers' notes

1) Lesson objective to simplify radicals in exact form.

2) Introducing three methods, prime factorization, largestsquare, and the calculator method.

Sue BlakelySmart Exemplary Educator

1296

Simplifying RadicalsSimplifying Radicals

54

To ThereTo There

From HereFrom Here

How Do We GetHow Do We Get

54 63

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

Simplifying RadicalsSimplifying Radicals

54Before 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 RadicalsSimplifying Radicals

13

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

This is an example of an "approximate" fraction.

but it is really .333333333333333333333333333333333333333333333333333333333333...

.33

Simplifying RadicalsSimplifying 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....

63

7.35

Simplifying RadicalsSimplifying Radicals

54This is a "square" root solet's find all the SQUARES

Find all the "Prime Factors" of the number 54, starting with the smallest prime.

2 3 3 3

23 32

Simplifying RadicalsSimplifying Radicals

54This is a "square" root solet's find all the SQUARES

Rewrite using square notations

2 3 32

Separate square root notations

Simplifying RadicalsSimplifying Radicals

54This is a "square" root solet's find all the SQUARES

OR...Rewrite and pull out the perfect squares

2 3 323

633

Simplifying RadicalsSimplifying Radicals

54This is a "square" root solet's find all the SQUARES

Multiply the remaining primes under the square root sign.

And You'reDone!!

And You'reDone!!

Simplifying RadicalsSimplifying Radicals

108Here Is Another Method

List all the perfect squares from 2 - 12.

22 = 432 = 942 = 1652 = 25

62 = 3672 = 4982 = 6492 = 81

102 = 100112 = 121122 = 144

22 = 432 = 942 = 1652 = 25

62 = 3672 = 4982 = 6492 = 81

102 = 100112 = 121122 = 144

Simplifying RadicalsSimplifying Radicals

108Here Is Another Method

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

Simplifying RadicalsSimplifying Radicals

108Here Is Another Method

Factor the two numbers to make the radical.

363

Simplifying RadicalsSimplifying Radicals

108Here Is Another Method

Rewrite and pull out the perfect squares.

363

62 = 36

6

Simplifying RadicalsSimplifying Radicals

252Lastly...The Calculator Method

Y=

22 5

X,T,Θ,n÷ x2

Simplifying RadicalsSimplifying Radicals

252Lastly...The Calculator Method

2nd GRAPH

The "y" sideis INSIDE

the radical signThe "x" sideis OUTSIDEthe radical sign

Simplifying RadicalsSimplifying Radicals

252Lastly...The Calculator Method

2nd GRAPH

Choose the lowest "y" INTEGER. Thereshould be no squares.

36 3

9 74 7

1 7

...no

...no

...no

...yes

76

Simplifying RadicalsSimplifying Radicals

Lastly.... The Calculator Method

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

And You'reDone!!

And You'reDone!!

252

The Best Part....... Choose What Is Easiest

For You

The Best Part....... Choose What Is Easiest

For You

1st: Factor all primes2nd: Factor perfect squares3rd: Calculator method

Practice ProblemsPractice Problems

162

1152 4329x

700-5

Practice ProblemsPractice Problems

320x3

918m4n7

972x2yz53xy

Teachers' notesLesson 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.

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.

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