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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