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4.2 and 4.3 Irational Numbers and Mixed.notebook
1
April 21, 2014
Unit 4: Powers and Roots
- Rational and Irrational numbe...
4.2 and 4.3 Irational Numbers and Mixed.notebook
2
April 21, 2014
Intro: Radicals
4.2 and 4.3 Irational Numbers and Mixed.notebook
3
April 21, 2014
4.2 Irrational Numbers
4.2 and 4.3 Irational Numbers and Mixed.notebook
4
April 21, 2014
Classifying Numbers...
4.2 and 4.3 Irational Numbers and Mixed.notebook
5
April 21, 2014
Rational Numbers: Have decimal representations that eith...
4.2 and 4.3 Irational Numbers and Mixed.notebook
6
April 21, 2014
Together, the set of rational and irrational numbers for...
4.2 and 4.3 Irational Numbers and Mixed.notebook
7
April 21, 2014
When an irrational number is written as a radical, the r...
4.2 and 4.3 Irational Numbers and Mixed.notebook
8
April 21, 2014
Example 1: Tell whether each number is rational or irrat...
4.2 and 4.3 Irational Numbers and Mixed.notebook
9
April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
10
April 21, 2014
Example 2: Use a number line to order these numbers fro...
4.2 and 4.3 Irational Numbers and Mixed.notebook
11
April 21, 2014
4.3 Mixed and Entire Fractions
4.2 and 4.3 Irational Numbers and Mixed.notebook
12
April 21, 2014
Multiplication Property of Radicals:
where n is a natur...
4.2 and 4.3 Irational Numbers and Mixed.notebook
13
April 21, 2014
We use this property to simplify square roots and cube ...
4.2 and 4.3 Irational Numbers and Mixed.notebook
14
April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
15
April 21, 2014
Radicals in the form areentire radicals
Radicals in the...
4.2 and 4.3 Irational Numbers and Mixed.notebook
16
April 21, 2014
Examples:
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
18
April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
Review: Simplifying Radicals
We can simplify a non­perf...
4.2 and 4.3 Irational Numbers and Mixed.notebook
22
April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
24
April 21, 2014
Some numbers, such as 200, have more than one perfect s...
4.2 and 4.3 Irational Numbers and Mixed.notebook
25
April 21, 2014
To write a radical of indexn in simplest form, we write...
4.2 and 4.3 Irational Numbers and Mixed.notebook
26
April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
4.2 and 4.3 Irational Numbers and Mixed.notebook
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April 21, 2014
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4.2 and 4.3 irrational numbers and simplifying radicals

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4.2 and 4.3 irrational numbers and simplifying radicals

  1. 1. 4.2 and 4.3 Irational Numbers and Mixed.notebook 1 April 21, 2014 Unit 4: Powers and Roots - Rational and Irrational numbers - Roots as exponents - Building on exponent law concepts
  2. 2. 4.2 and 4.3 Irational Numbers and Mixed.notebook 2 April 21, 2014 Intro: Radicals
  3. 3. 4.2 and 4.3 Irational Numbers and Mixed.notebook 3 April 21, 2014 4.2 Irrational Numbers
  4. 4. 4.2 and 4.3 Irational Numbers and Mixed.notebook 4 April 21, 2014 Classifying Numbers...
  5. 5. 4.2 and 4.3 Irational Numbers and Mixed.notebook 5 April 21, 2014 Rational Numbers: Have decimal representations that either terminate or repeat. Irrational Numbers: cannot be written in the form m/n, where m and n are integers and n ≠ 0. The decimal representation of an irrational number neither terminates nor repeats.
  6. 6. 4.2 and 4.3 Irational Numbers and Mixed.notebook 6 April 21, 2014 Together, the set of rational and irrational numbers form the set of real numbers.
  7. 7. 4.2 and 4.3 Irational Numbers and Mixed.notebook 7 April 21, 2014 When an irrational number is written as a radical, the radical is the exact value of the irrational number. Use the method practiced in Lab 1 to approximate irrational numbers and their location on the number line.
  8. 8. 4.2 and 4.3 Irational Numbers and Mixed.notebook 8 April 21, 2014 Example 1: Tell whether each number is rational or irrational and explain.
  9. 9. 4.2 and 4.3 Irational Numbers and Mixed.notebook 9 April 21, 2014
  10. 10. 4.2 and 4.3 Irational Numbers and Mixed.notebook 10 April 21, 2014 Example 2: Use a number line to order these numbers from least to greatest.
  11. 11. 4.2 and 4.3 Irational Numbers and Mixed.notebook 11 April 21, 2014 4.3 Mixed and Entire Fractions
  12. 12. 4.2 and 4.3 Irational Numbers and Mixed.notebook 12 April 21, 2014 Multiplication Property of Radicals: where n is a natural number, and a and b are real numbers
  13. 13. 4.2 and 4.3 Irational Numbers and Mixed.notebook 13 April 21, 2014 We use this property to simplify square roots and cube roots that are not perfect squares or perfect cubes, but have factors that are perfect squares or perfect cubes. Examples:
  14. 14. 4.2 and 4.3 Irational Numbers and Mixed.notebook 14 April 21, 2014
  15. 15. 4.2 and 4.3 Irational Numbers and Mixed.notebook 15 April 21, 2014 Radicals in the form areentire radicals Radicals in the form aremixed radicals.
  16. 16. 4.2 and 4.3 Irational Numbers and Mixed.notebook 16 April 21, 2014 Examples:
  17. 17. 4.2 and 4.3 Irational Numbers and Mixed.notebook 17 April 21, 2014
  18. 18. 4.2 and 4.3 Irational Numbers and Mixed.notebook 18 April 21, 2014
  19. 19. 4.2 and 4.3 Irational Numbers and Mixed.notebook 19 April 21, 2014
  20. 20. 4.2 and 4.3 Irational Numbers and Mixed.notebook 20 April 21, 2014
  21. 21. 4.2 and 4.3 Irational Numbers and Mixed.notebook 21 April 21, 2014 Review: Simplifying Radicals We can simplify a non­perfect radical by converting it from an  entire radical to a mixed radical
  22. 22. 4.2 and 4.3 Irational Numbers and Mixed.notebook 22 April 21, 2014
  23. 23. 4.2 and 4.3 Irational Numbers and Mixed.notebook 23 April 21, 2014
  24. 24. 4.2 and 4.3 Irational Numbers and Mixed.notebook 24 April 21, 2014 Some numbers, such as 200, have more than one perfect square factor. The question is: which combination do we use?
  25. 25. 4.2 and 4.3 Irational Numbers and Mixed.notebook 25 April 21, 2014 To write a radical of indexn in simplest form, we write the radicand as a product of 2 factors, one of which is the greatest perfect nth power.
  26. 26. 4.2 and 4.3 Irational Numbers and Mixed.notebook 26 April 21, 2014
  27. 27. 4.2 and 4.3 Irational Numbers and Mixed.notebook 27 April 21, 2014
  28. 28. 4.2 and 4.3 Irational Numbers and Mixed.notebook 28 April 21, 2014

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