Post on 18-May-2015
4.2 and 4.3 Irational Numbers and Mixed.notebook
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Unit 4: Powers and Roots
- Rational and Irrational numbers- Roots as exponents- Building on exponent law concepts
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Intro: Radicals
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4.2 Irrational Numbers
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Classifying Numbers...
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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.
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Together, the set of rational and irrational numbers form the set of real numbers.
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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.
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Example 1: Tell whether each number is rational or irrational and explain.
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Example 2: Use a number line to order these numbers from least to greatest.
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4.3 Mixed and Entire Fractions
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Multiplication Property of Radicals:
where n is a natural number, and a and b are real numbers
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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:
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Radicals in the form are entire radicals
Radicals in the form are mixed radicals.
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Examples:
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Review: Simplifying Radicals
We can simplify a nonperfect radical by converting it from an entire radical to a mixed radical
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Some numbers, such as 200, have more than one perfect square factor. The question is: which combination do we use?
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To write a radical of index n in simplest form, we write the radicand as a product of 2 factors, one of which is the greatest perfect nth power.
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