Simplify Radicals Lesson objectives Teachers' notes 1) Lesson objective to simplify radicals in exact form. 2) Introducing three methods, prime factorization,
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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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