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# May 5, 2014

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### May 5, 2014

1. 1.  Review for Quadratics re-take Tomorrow  Radical Operations  Class/Home Work Today: May 5, 2014
2. 2. Quadratic Formula Review −𝒃 ± 𝒃 𝟐 − 𝟒𝒂𝒄 𝟐𝒂- 6 = -8x – 6x2 6x2 + 8x – 6 = 0 −𝟖 ± 𝟔𝟒 + 𝟏𝟒𝟒 𝟏𝟐 −𝟖 ± 𝟐𝟎𝟖 𝟏𝟐 −𝟖 ± 𝟒 𝟏𝟑 𝟏𝟐 −𝟐 ± 𝟏𝟑 𝟑
3. 3. Quadratic Formula Review −𝟓 ± 𝟐𝟓 + 𝟐𝟎𝟎 𝟐 w(w + 5) = 50 w2 + 5w – 50 = 0 −𝟓 ± 𝟏𝟓 𝟐width = 5; length = 10
4. 4. 4x2 – 4 = 26 30 4 30 4 x = + 30 2 Quadratic Formula Review -1 – 5m2 = - 23 Can there be a solution to this problem? 22 5 m2 = 22 5 22 5 • 5 5 x = + 110 5
5. 5. Class Notes Section of Notebook
6. 6. NOTE: Every positive real number has two real number square roots. The number 0 has just one square root, 0 itself. Negative numbers do not have real number square roots. When simplifying we choose the positive value of 𝒂 called the principal root. 13169  00  RootsRNo eal4  Simplify 169 13 Note, since we are evaluating, we only use the positive answer.
7. 7. Simplifying Radical Expressions by Multiplying or Dividing
8. 8. Simplifying Radicals Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. Separate Combine A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.
9. 9. Simplifying Radicals Simplify the expression.
10. 10. Simplifying Radicals w/Variables 32x5y3z2 =Practice:Review: 25 x 17 27x12 x x 8 3 3x x 6 7 3 16x x Bronze Level Silver Level Gold Level 3 2 2 2 2                 x x x x x x x x x x x x x 3 2 2 2 2                 x x x x x x x x x x x x x 2 2 3       x x x x x x x 6 4 3x x 4x2yz xy
11. 11. If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator. Multiply by a form of 1. Rationalizing the Denominator • 𝟓 𝟓 = 60 = 5
12. 12. Simplify the expression. Rationalizing the Denominator Remember: Note: Try to simplify first before automatically trying to rationalize a radical denominator.
13. 13. Simplify by rationalizing the denominator. Multiply by a form of 1.
14. 14. Rationalizing a Binomial Denominator Big picture: To remove the radical, we multiply the binomial by another binomial, (FOIL) called its conjugate. The conjugate is simply the same binomial with the sign changed between terms.
15. 15. Multiply the Conjugates Conjugates x2 = 9 y2 = (2 𝟓)(2 𝟓) = 20 9 – 20 = -13 Practice: 8 – 14 = -6 The middle terms always cancel each other out so you don’t really have to FOIL.
17. 17. Add . Adding & Subtracting Radicals Can these radicals be added? 𝟔 + 𝟔 𝟔 = 12 𝟔 = 𝟔 + 𝟔 𝟔 𝟑 𝟑 ± 𝟑 𝟔 𝟑 =𝟏 ± 𝟔