1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-1 Roots, Radicals, and Complex Numbers Chapter 7

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – 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 Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-3 § 7.6 Solving Radical Equations

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-4 Solve Equations Containing One Radical Radical Equation A radical equation is an equation that contains a variable in a radicand. Examples of Radical Equations

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-5 Solve Equations Containing One Radical To Solve Radical Equations 1.Rewrite the equation so that one radical containing a variable is by itself (isolated) on one side of the equation. 2.Raise each side of the equation to a power equal to the index of the radical. 3.Combine like terms. 4.If the equation still contains a term with a variable in a radicand, repeat steps 1 through 3. 5.Solve the resulting equation for the variable. 6.Check all solutions in the original equation for extraneous solutions.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-6 Solve Equations Containing Two Radicals Example Solve

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-7 Solve Equations Containing Two Radical Terms and a Nonradical Term Example Solve We must isolate one radical term on one side of the equation. We will begin by adding to both sides of the equation to isolate. Then we will square both sides of the equation and combine like terms. continued

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-8 Solve Equations Containing Two Radical Terms and a Nonradical Term continued We have isolated the remaining radical term. We now square both sides of the equation again and solve for x.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-9 Solve Equations Containing Two Radical Terms and a Nonradical Term

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-10 Solve Applications Using Radical Equations Example In Fenway Park, where the Boston Red Sox play baseball, the distance from the home plate down the third base line to the bottom of the wall in left field is 310 feet. In left field at the end of the baseline there is a green wall perpendicular to the ground that is 37 feet tall. This green wall is common known as the Green Monster (see photo). Determine the distance from home plate to the top of the Green Monster along the third base line. continued

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-11 Solve Applications Using Radical Equations To solve the problem we use the Pythagorean Theorem, which was discussed earlier: leg 2 + leg 2 = hyp 2, or a 2 + b 2 = c 2. continued

12 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 7-12 Solve Applications Using Radical Equations The distance from home plate to the top of the wall is about feet.