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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, largest square, and the calculator method. Sue Blakely Smart Exemplary Educator

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12 96 Simplifying Radicals 54

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To There From Here How Do We Get 54 6 3

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

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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.

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Simplifying Radicals 1313 This is an example of an "exact form" fraction. This is an example of an "approximate" fraction. but it is really.3333333333333333333333333333333 33333333333333333333333333333....33

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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 7.35

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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 33

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2 3 3 2 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 notations

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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 3

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6 3 3 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!!

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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

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22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 112 = 121 122 = 144 Simplifying Radicals 108 Here Is Another Method Find the largest perfect square that will divide evenly into the radical.

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Simplifying Radicals 108 Here Is Another Method Factor the two numbers to make the radical. 36 3

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Simplifying Radicals 108 Here Is Another Method Rewrite and pull out the perfect squares. 36 3 62 = 36 6

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Simplifying Radicals 252 Lastly... The Calculator Method Y= 2 2 5 X,T,Θ,n ÷ x2

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Simplifying Radicals 252 Lastly... The Calculator Method 2nd GRAPH The "y" side is INSIDE the radical sign The "x" side is OUTSIDE the radical sign

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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...yes

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7 6 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!! 252

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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 method

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Practice Problems 162 1152 432 9x9x 700 -5

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Practice Problems 320x3 918m4n7 972x2yz5 3xy

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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. 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. an imations from www.gifanimations.com, www.animatedgif.net (touch text to see copyright information)

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gifanimations.com Image Linking and Usage Policy Image Usage All images contained within the GIFAnimations collection are in the public domain. We do not require you to obtain our permission to use any of these images. Images may be used in any media (web site, email, powerpoint, print, etc.) Our images can be used by any entity (i.e., commercial, non-profit, educational, governmental, religious, etc.) We do appreciate any credit that you may give to GIFAnimations.com on your web page, but this is not required for image use. www.animatedgif.net COPYRIGHTS: As far as we know, all the animations in this site (including those we've created) are public domain images. AUTHORS: If you find an animation in this collection that is yours, we want to recognize, salute and promote you and your art.. Please Email us. As you desire, we will either list your name with the animation (linked to your own site), or will remove the image. We want to promote your images and your name! We also want to refer design work to you. Please join our network of artists to whom we refer our design inquiries (we don't do that kind of work in-house anymore.)

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