1. Example 1: Solving Equations Containing One Radical
Objective
Solve radical equations and inequalities.
SOLVING RADICAL EQUATIONS:
#1: _______ the _______
#2: Raise both sides to the _________ of the ________.
Example 1: Solving Equations Containing One Radical
Solve each equation. Check your answer on your calculator. A. B. C.

2. Example 2: Solving Equations Containing Two Radicals
Solve and check your answer on your calculator. A. B. C.

3. Example 3: Solving Equations with Extraneous Solutions
Raising each side of an equation to an even power may
introduce ______________ solutions.
Example 3: Solving Equations with Extraneous Solutions
A. Solve
Method 1 Use a graphing calculator.
Method 2 Use algebra to solve the equation.
B. Solve the equation.
Method 1 Use a graphing calculator.
Method 2 Use algebra to solve the equation.

4. Example 4: Solving Equations with Rational Exponents
C. Solve.
Example 4: Solving Equations with Rational Exponents
Solve each equation.
(5x + 7) = 3 1 3
2x = (4x + 8) 1 2 A. B.
C. (x + 5) = 3 1 3

5. Example 5: Solving Radical Inequalities
A. Solve
Method 1 Use a graph and a table.
Method 2 Use algebra to solve the inequality.
B. Solve.
Method 1 Use a graph and a table.
Method 2 Use algebra to solve the inequality.
Example 6: Application
The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula s = , where f is the coefficient of friction and d is the length of the skid marks in feet.
A car skids to a stop on a street with a speed limit of 30 mi/h. The skid marks measure 35 ft, and the coefficient of friction was 0.7. Was the car speeding? Explain. 30 fd