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 Review for Quadratics re-take Tomorrow
 Radical Operations
 Class/Home Work
Today:
May 5, 2014
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 ± ...
Quadratic Formula Review
−𝟓 ± 𝟐𝟓 + 𝟐𝟎𝟎
𝟐
w(w + 5) = 50
w2 + 5w – 50 = 0
−𝟓 ± 𝟏𝟓
𝟐width = 5; length = 10
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
m...
Class Notes Section of Notebook
NOTE: Every positive real number has two real number
square roots.
The number 0 has just one square root, 0 itself.
Negati...
Simplifying Radical Expressions by
Multiplying or Dividing
Simplifying Radicals
Notice that these properties can be used to combine
quantities under the radical symbol or separate t...
Simplifying Radicals
Simplify the expression.
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 L...
If a fraction has a denominator that is a square
root, you can simplify it by rationalizing the
denominator.
To do this, m...
Simplify the expression.
Rationalizing the Denominator
Remember:
Note: Try to simplify first before automatically
trying t...
Simplify by rationalizing the denominator.
Multiply by a form of 1.
Rationalizing a Binomial
Denominator
Big picture: To remove the radical, we multiply the
binomial by another binomial, (FO...
Multiply the Conjugates
Conjugates
x2 = 9
y2 = (2 𝟓)(2 𝟓) = 20 9 – 20 = -13
Practice: 8 – 14 = -6
The middle terms always ...
Square roots that have the same radicand are called
like radical terms.
To add or subtract square roots, simplify each rad...
Add
.
Adding & Subtracting Radicals
Can these radicals be added?
𝟔 + 𝟔 𝟔 = 12 𝟔 = 𝟔 + 𝟔 𝟔
𝟑
𝟑
± 𝟑 𝟔
𝟑
=𝟏 ± 𝟔
Subtract.
Simplify radical terms.
Adding & Subtracting Radicals
Simplify radical terms.
Word Problem
A stadium has a square poster of a football player
hung from the outside wall. The poster has an area of
12,5...
Class Work:
See Handout
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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.
  16. 16. Square roots that have the same radicand are called like radical terms. To add or subtract square roots, simplify each radical term and then combine like radical terms by adding or subtracting their coefficients. Adding & Subtracting Radicals You can only add or subtract radicals that have the same radicand. The coefficients are combined, the radicand stays the same. (Like the denominator of a fraction) Example: = 5 ? Does 𝟑 𝟓 - 𝟐 𝟓 = 1? = 4 𝟑
  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
  18. 18. Subtract. Simplify radical terms. Adding & Subtracting Radicals Simplify radical terms.
  19. 19. Word Problem A stadium has a square poster of a football player hung from the outside wall. The poster has an area of 12,544 ft2. What is the width of the poster? 112 feet wide
  20. 20. Class Work: See Handout

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