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Solving Square Root and Radical Equations: A Comprehensive Guide

In this chapter, we explore radical equations and methods for solving them, including those with rational exponents. A radical equation contains a variable under a root or expressed with a rational exponent. Key steps include isolating the radical, raising both sides to the index power, solving for the variable, and verifying solutions to avoid extraneous results. Through various examples, we illustrate these concepts, including real-world applications like determining the radius of a solar cell to meet power requirements.

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Solving Square Root and Radical Equations: A Comprehensive Guide

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  1. Chapter 6 Radical Functions and Rational Exponents

  2. 6-5 Solving Square Root and other Radical Equations What you’ll learn … • To solve radical equations

  3. 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

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

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

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

  7. 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?

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

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

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