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Chapter 6 Radical Functions and Rational Exponents

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6-5 Solving Square Root and other Radical Equations What you’ll learn … To solve radical equations

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A radical equation is an equation that has a variable in a radicand or has a variable with a rational exponent. Radical Equation Not a Radical Equation

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Steps for Solving a Radical Equation 1. Get radical by itself. 2. Raise both sides to index power. 3. Solve for x. 4. Check.

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Example 1 Solving Radical Equations with Index 2 Solve 2 + √3x-2 = 6 √5x+1 – 6 = 0

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Example 2 Solving Radical Equations with Rational Exponents Solve 2 (x – 2) 2/3 = 50 3(x+1) 3/5 = 24

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Real World Connection A company manufactures solar cells that produce 0.02 watts of power per square centimeter of surface area. A circular solar cell needs to produce at least 10 watts. What is the minimum radius?

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Example 4 Checking for Extraneous Solutions Solve √x – 3 + 5 = x √3x + 2 - √2x + 7 = 0

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Example 5 Solving Equations with Two Rational Exponents Solve (2x +1) 0.5 – (3x+4) 0.25 = 0 Solve (x +1) 2/3 – (9x+1) 1/3 = 0

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