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Roots, Radicals, and Complex Numbers
Chapter 7 Roots, Radicals, and Complex Numbers
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Chapter Sections 7.1 – Roots and Radicals 7.2 – Rational Exponents
7.3 – Simplifying Radicals 7.4 – Adding, Subtracting, and Multiplying Radicals 7.5 – Dividing Radicals 7.6 – Solving Radical Equations 7.7 – Complex Numbers Chapter 1 Outline
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7.6: Solving Radical Equations
1. Solve Radical Equations 2. Solve Equations Containing One Radical 3. Solve Equations Containing Two Radicals 4. Solve Applications using Radical Equations.
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Solve Equations Containing One Radical
Radical Equation A radical equation is an equation that contains a variable in a radicand. Example 1: To Solve Radical Equations Rewrite the equation to isolate the radical. Raise each side of the equation to a power equal to the index of the radical. Combine like terms. Repeat the steps, if need be. Solve. Check all solutions in the original equation Check
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Example 2: Solve Check Check True
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Example 3: Solve Check: Does it Check? False. True.
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Solve Equations Containing Two Radicals
Example 4: Solve Check: Check:
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Solve Equations Containing Two Radical Terms and a Non-radical Term
Example 5: Solve Check There is no solution.
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Solve Equations Containing Two Radical Terms and a Non-radical Term
Example 6: Solve
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Example 7: Solve for the indicated variable.
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Solve Applications Using Radical Equations
Determine the hypotenuse in the figure below. Use the Pythagorean Theorem: a2 + b2 = c2.
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Solve Applications Using Radical Equations
Use the Pythagorean Theorem: a2 + b2 = c2.
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