This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The distinction between the principal square root of the number x and the secondary square root of the number x is made by explanation and by example. The simplification of the radical expressions that both involve and do not involve fractions is shown in many detailed examples; this is followed by an explanation of how and why radicals are eliminated from the denominator of a radical expression. Real-life applications of radical equations have been included, such as problems involving daily output, daily sales, electronic resonance frequency, and kinetic energy.This module contains the objectives for the chapter "Roots, Radicals, and Square Root Equations".
After completing this chapter, you should
Square root expressions (
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- understand the concept of square root
- be able to distinguish between the principal and secondary square roots of a number
- be able to relate square roots and meaningful expressions and to simplify a square root expression
Simplifying square root expressions (
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- be able to identify a perfect square
- be familiar with the product and quotient properties of square roots
- be able to simplify square roots involving and not involving fractions
Multiplication of square root expressions (
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- be able to use the product property of square roots to multiply square roots
Division of square root expressions (
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- be able to use the division property of square roots, the method of rationalizing the denominator, and conjugates to divide square roots
Addition and subtraction of square root expressions (
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- understand the process used in adding and subtracting square roots
- be able to add and subtract square roote
Square root equations with applications (
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- be able to recognize square root equations and extraneous solutions
- be able to solve square root equations
