Chapter 7 Roots Radicals and Complex Numbers 1

Chapter 7 Roots, Radicals, and Complex Numbers 1

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 2

7. 6: Solving Radical Equations t t 1. Solve Radical Equations 2. Solve Equations Containing One Radical 3. Solve Equations Containing Two Radicals 4. Solve Applications using Radical Equations.

Solve Equations Containing One Radical Equation A radical equation is an equation that contains a variable in a radicand. Example 1: To Solve Radical Equations 1. Rewrite the equation to isolate the radical. 2. Raise each side of the equation to a power equal to the index of the radical. 3. Combine like terms. 4. Repeat the steps, if need be. 5. Solve. 6. Check all solutions in the original equation Check

Example 2: Solve Check True

Example 3: Solve Check: Does it Check? False. True.

Solve Equations Containing Two Radicals Example 4: Solve Check:

Solve Equations Containing Two Radical Terms and a Non-radical Example 5: Solve Term Check There is no solution.

Solve Equations Containing Two Radical Terms and a Non-radical Term Example 6: Solve

Example 7: Solve for the indicated variable.

Solve Applications Using Radical Equations Determine the hypotenuse in the figure below. Use the Pythagorean Theorem: a 2 + b 2 = c 2.

Solve Applications Using Radical Equations Use the Pythagorean Theorem: a 2 + b 2 = c 2.