1. Roots, Radicals, and Complex Numbers
Chapter 7
Roots, Radicals, and Complex Numbers

2. 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
Chapter 1 Outline

3. 7.6: Solving Radical Equations
1. Solve Radical Equations
2. Solve Equations Containing One Radical
3. Solve Equations Containing Two Radicals
4. Solve Applications using Radical Equations.

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

5. Example 2: Solve
Check
Check
True

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

7. Solve Equations Containing Two Radicals
Example 4: Solve
Check:
Check:

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

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

10. Example 7: Solve for the indicated variable.

11. Solve Applications Using Radical Equations
Determine the hypotenuse in the figure below.
Use the Pythagorean Theorem: a2 + b2 = c2.

12. Solve Applications Using Radical Equations
Use the Pythagorean Theorem: a2 + b2 = c2.