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**5.7 Rational Exponents 5.8 Radical equations**

Algebra II w/ trig

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Rational (fraction) exponents can be rewritten in radical form, and radicals can be rewritten in rational form.

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I. Write in radical form. A. B. C. D. E.

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**II. Write in exponential form. A. B. C. D. E. **

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III. Evaluate. A. B. C. D.

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E. F.

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**IV. Conditions for a simplified expression**

--it has no negative exponents --it has no fractional exponents in denominator --it is not a complex fraction --the index of any remaining radical is small as possible ***if the original problem is in radical form, the answer should be in radical form*** ***If the problem is in rational exponent form, the answer should be in rational form***

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A. B.

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C. D.

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E. F.

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5.8 Rational expressions I. Definitions: 1. Radical equations is an equation that has a variable in a radicand. Ex: Not: 2. Extraneous solutions is a solution that does not satisfy the original equation. You can only determine if a solution is extraneous by checking your answer.

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**II. Steps to Solving Radical Equations:**

A. Isolate the radical if possible. B. To eliminate the radical, raise each side of the equation to a power equal to the index of the radical. C. Solve the resulting equation. D. Check for extraneous solutions.

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**III. Solving a simple radical equation.**

A. B.

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C. D.

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**IV. Solving an equation with one radical. A. B. **

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**V. Solving an Equation with two radicals.**

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**Steps to Solving Radical Inequalities**

A. If the index of the root is even, identify the values of the variable for which the radicand is nonnegative. B. Solve the inequality algebraically. C. Test values to check your solution.

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**Solve each inequality: A. B.**

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HW: 5.7 Worksheet (on the back of the factoring ws) Page 266 #13-28 all Start studying for Chapter 5 Test on Friday

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Rational Exponents, Radicals, and Complex Numbers

Rational Exponents, Radicals, and Complex Numbers

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