Simplify Radicals 1 Lesson objective to simplify radicals

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 Radicals 54 96 2 1

How Do We Get From Here To There 54 3 6

I KNOW, 
pick me, pick me!!!

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 
 approximate numbers.

Simplifying 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 
. 3333333333333333. . .

Simplifying 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. .

Simplifying 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 Radicals 54 This is a "square" root so let's find all the SQUARES Rewrite using square notations 3 2 Separate square root notations 3 2 2 3

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

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

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

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

Simplifying Radicals 252 2 nd 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 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 1 st: Factor all primes 2 nd: Factor perfect squares 3 rd: Calculator method

Practice Problems 162 -5 700 1152 9 x 432

Practice Problems 320 x 3 918 m 4 n 7 3 xy 972 x 2 yz 5

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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