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Radicals 07/27/12lntaylor ©. Table of Contents Learning Objectives Parts of a Radical Simplifying Radicals Radical Expressions Estimating Radicals Practice.

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Presentation on theme: "Radicals 07/27/12lntaylor ©. Table of Contents Learning Objectives Parts of a Radical Simplifying Radicals Radical Expressions Estimating Radicals Practice."— Presentation transcript:

1 Radicals 07/27/12lntaylor ©

2 Table of Contents Learning Objectives Parts of a Radical Simplifying Radicals Radical Expressions Estimating Radicals Practice 07/27/12lntaylor ©

3 LO1: LO2: Define and differentiate radicals, radicands and root index Estimate and simplify radical expressions 07/27/12lntaylor © TOC Learning Objectives

4 PK1:Knowledge of exponent operations 07/27/12lntaylor © TOC Previous Knowledge

5 Def1: Def2: 07/27/12lntaylor © TOC Parts of a Radical Expression (Definitions) Def3:

6 07/27/12lntaylor © TOC Simplifying Radicals Step1:To simplify a radical you must first know your perfect squares Step2:Only then will you understand the square roots Step3:Memorize the following charts (perfect squares and square roots)

7 07/27/12 lntaylor © TOC SquaresEquivalents > 4 > > > > > 9 16 25 36 49 > 64 > 81 > 100 > > > > > 121 144 169 196 225 clear answers

8 07/27/12 lntaylor © TOC Square RootsEquivalents > 2 > > > > > 3 4 5 6 7 > 8 > 9 > 10 > > > > > 11 12 13 14 15 clear answers

9 07/27/12lntaylor © TOC Square RootsEquivalents > 2 > > > > > 3 4 5 6 7 > 8 > 9 > 10 > > > 11 12 13 note Do you see that the square root of a number squared is that number? clear answers

10 Step1: Step2: This radicand (24) is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of 24? 07/27/12lntaylor © TOC Step3:Hint: Only one combination includes a perfect square Rewrite the problem with 2 radicals Step4:Simplify (reduce) the radical containing the perfect square Leave the other alone Step5:This is your final answer 24 24 =2(12) 3(8) 4(6)

11 07/26/12lntaylor © TOC

12 Step1: Step2: This radicand (28) is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of 28? 07/27/12lntaylor © TOC Step3:Hint: Only one combination includes a perfect square Rewrite the problem with 2 radicals Step4:Simplify (reduce) the radical containing the perfect square Leave the other alone Step5:This is your final answer 28 28 =2(14) 3(not a whole number) 4(7)

13 07/26/12lntaylor © TOC

14 Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with 3 radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer 72 72 =9(8) 9(4)(2)

15 07/26/12lntaylor © TOC

16 Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with 3 radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer 675 675 =25(27) 25(9)(3)

17 07/26/12lntaylor © TOC

18 Step1: Step2: This radicand is not a perfect square Therefore – find the perfect square! Start by factoring the radicand into a perfect square times a number What are the factors of the radicand? 07/27/12lntaylor © TOC Step3:Hint: make sure you factor out all perfect squares! Rewrite the problem with radicals Step4:Simplify (reduce) any radicals containing the perfect squares Leave the other alone Step5:This is your final answer 160 160 =16(10)

19 07/27/12lntaylor © TOC Radical Expressions Step1:To simplify radical expressions you must first understand exponents Step2:Only then will you understand the radical expressions Step3:Memorize the following charts (square root exponents)

20 07/27/12lntaylor © TOC Square RootsEquivalents > 2x > > > > > > > 2xy > > > note Do you see that the square root of an even exponent is half the exponent; the square root of an odd exponent puts half the exponent outside the radical and leaves an exponent of 1 under the radical? clear answers

21 07/27/12lntaylor © TOC Radical Expressions Note:If you understood the preceding chart then you are ready to go on!

22 07/26/12lntaylor © TOC

23 Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Simplify the problem Step4:This is your final answer 2x(3y) 6xy

24 07/26/12lntaylor © TOC

25 Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Simplify the problem Step4:This is your final answer (9y)

26 07/26/12lntaylor © TOC

27 Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring the perfect squares out of each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Rewrite the problem Cancel any terms Step4:This is your final answer

28 07/26/12lntaylor © TOC

29 Step1: Step2: To do these properly you must “unpack” each part of the expression There are 2 parts here! Start by factoring the perfect squares out of each radicand 07/27/12lntaylor © TOC Step3:Hint: make sure you have factored out all perfect squares! Rewrite the problem Cancel any terms Step4:This is your final answer

30 07/27/12lntaylor © TOC Estimating Radicals

31 Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands(64 – 49) This becomes the denominator Subtract the middle radicand (60) from the lower radicand (49) This becomes the numerator Estimate the decimal equivalent of the fraction Step4: 7 8 64 – 49 = 15 __ 15 60 – 49 = 11 11 ≈ 0.75 7.75

32 07/26/12lntaylor © TOC

33 Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands(100 – 86) This becomes the denominator Subtract the middle radicand (86) from the lower radicand (81) This becomes the numerator Estimate the decimal equivalent of the fraction Step4: 9 10 100 – 81 = 19 __ 19 86 – 81 = 5 5 ≈ 0.25 9.25

34 07/26/12lntaylor © TOC

35 Step1: Step2: Estimating a radical is not difficult First figure out which two perfect squares it lies between Factor the perfect squares onto a number line 07/27/12lntaylor © TOC Step3:Find the range between the perfect square radicands This becomes the denominator Subtract the middle radicand from the lower radicand This becomes the numerator Estimate the decimal equivalent of the fraction Step4: 14 15 225 – 196 = 29 __ 29 200 – 196 = 4 4 ≈ 0.14 14.14

36 07/27/12lntaylor © TOC Practice

37 07/27/12lntaylor © TOC ProblemAnswer > ≈ 5.78 > > > > > ≈ 7.14 2 2 > ≈ 4.44 > > clear answers

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