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Solve radical equations and inequalities.

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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.

Example 2: Solving Equations Containing Two Radicals

Solve and check your answer on your calculator.

A.

B.

C.

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.

1

2

2x = (4x + 8)

1

1

3

3

C. (x + 5) = 3

(5x + 7) = 3

C. Solve.

Example 4: Solving Equations with Rational Exponents

Solve each equation.

A.

B.

A. Solve. .

30

fd

Example 5: Solving Radical Inequalities

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.