What's Going On? What's Radical. Radicals Dude! Thinking About the End. Learning Goal I will be able to simplify radical expressions.

Transcription

1 What's Going On? What's Radical Radicals Dude! Thinking About the End Learning Goal I will be able to simplify radical expressions. 1

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3 Identify the option that most accurately represents "radical". a) b) c) d) 3

4 In math, a radical is just a fancy word to describe a root. Radicals can be square roots: cube roots: fourth roots: n th roots: 4

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6 Essentially, a radical represents the opposite operation of applying an exponent. To 'simplify' the radical, you need to ask yourself: "What number when multiplied by itself 'n' times, equals x?" Or... use your calculator! Example What is the 6th root of 729? 6

7 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** 7

8 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 8

9 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 9

10 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 10

11 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 11

12 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 12

13 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** 13

14 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 14

15 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 15

16 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** 16

17 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 17

18 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 18

19 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. is "wrong"! Think of it like an improper fraction. NO IN THE DENOMINATOR OR ELSE... We need to RATIONALIZE the denominator... 19

20 A Few Important Laws NO IN THE DENOMINATOR!!!! We need to RATIONALIZE the denominator... 20

21 A Few Important Laws ***THINK OF THE VALUE UNDER THE ROOT SIGN AS A VARIABLE. TREAT THEM AS LIKE/UNLIKE TERMS*** Simplify. 21

22 Simplifying Radicals Simplify (no decimals) = 6 Simplify (no decimals) =??? 22

23 Simplifying Radicals Just like with fractions, we always want to represent radicals in lowest terms If the number under a root sign can be represented as a product of multiple integers, where one integer is a perfect square, cube, etc... it is not yet simplified! = = = No foolin'! Check it on your calculator! 23

24 Simplify. 24

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31 Simplify. 31

32 Simplify. 32

33 Simplify. 33

34 Simplify. 34

35 The Course in Review You will be split into 6 even groups. Each group will be given one unit to focus on. Your group will produce a unit review for the class. You must include the key concepts, examples and questions! 35

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37 The Course in Review Unit 1: Trigonometry Unit 2: Linear Systems Unit 3: Analytic Geometry Unit 4: Polynomials Unit 5: Quadratics I Unit 6: Quadratics II 37

38 The Course in Review Unit 1: Trigonometry - Similar triangles - sohcahtoa - Sine Law - Cosine Law 38

39 The Course in Review Unit 2: Linear Systems - Points of Intersection - Solving by Graphing - Solving by Substitution - Solving by Elimination 39

40 The Course in Review Unit 3: Analytic Geometry - Length of Line Segments - Midpoints of Line Segments - Right Bisector, Median, Altitude - Circumcentre, Centroid, Orthocentre - Distance from a point to a line - Equations of Circles 40

41 The Course in Review Unit 4: Polynomials - Exponent Laws - Expanding Binomials (FOIL) - Factoring 41

42 The Course in Review Unit 5: Quadratics I - Functions - Vertex Form Equations (a, h and k) - Completing the Square - First and Second Differences 42

43 The Course in Review Unit 6: Quadratics II - "Solving" Quadratic Equations - by graphing - by factoring - using the Quadratic Formula - The Discriminant 43

44 Attachments qxu82kok.bmp