Accident Investigation

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5-8 solving radical equations and inequalities

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Accident Investigation Example 4 Using Radical Expressions Accident Investigation After a car accident, a police officer measures the length l (in feet) of a car’s skid marks. The expression gives the car’s speed in miles per hour at the time the brakes were applied. 27l a. Write the expression in simplest form. b. The skid marks are 125 feet long. Use the simplified expression to approximate the car’s speed when the brakes were applied.

Example 4 SOLUTION = 27l 9 • 3 l a. = • 3l 9 = 3 3l ANSWER Using Radical Expressions SOLUTION Factor using greatest perfect square factor. = 27l 9 • 3 l a. Product property of square roots = • 3l 9 Simplify. = 3 3l ANSWER In simplest form, 27l = 3 3l . 2

The car’s speed was about 58 miles per hour. Example 4 Using Radical Expressions b. 3 3l = 3 • 125 Substitute 125 for l. Multiply. 375 3 = Approximate using a calculator. ≈ 58 ANSWER The car’s speed was about 58 miles per hour. 3