Write the radical expression in simplest form.

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Presentation transcript:

Write the radical expression in simplest form. Example 1 Simplifying Radical Expressions Write the radical expression in simplest form. a. 250 b. 108 Factor out greatest perfect square factor. SOLUTION a. 250 = 25 • 10 = 25 • Product property of square roots 10 = 5 10 Simplify. Factor out greatest perfect square factor. b. 108 = 36 • 3 = 36 • 3 Product property of square roots 3 = Simplify. 6

a. Write the expression in simplest form. Example 2 Using a Radical Expression in Real Life WALKING SPEED A person’s maximum walking speed (in inches per second) can be approximated using the expression 384l where l is the person’s leg length (in inches). a. Write the expression in simplest form. b. Use the simplified expression to approximate the maximum walking speed of a person whose leg length is 29 inches. Factor out greatest perfect square factor. SOLUTION a. 384l = 64 • 6l

Example 2 = 64 • 6l = 6l 8 ANSWER In simplest form, 384l = 6l 8 b. 6l Using a Radical Expression in Real Life = 64 • 6l Product property of square roots = 6l Simplify. 8 ANSWER In simplest form, 384l = 6l 8 b. 6l 8 Substitute 29 for l. = 6 • 29 = 174 Multiply. 8 106 Approximate using a calculator. ≈ ANSWER The person’s maximum walking speed is approximately 106 inches per second.

Simplify the radical expression 5 • 10. Example 3 Simplifying a Product of Two Radicals Simplify the radical expression 5 • 10. 5 • 10 = 50 Product property of square roots = 25 • 2 Factor out greatest perfect square factor. = 25 • Product property of square roots 2 = 2 Simplify. 5

Simplify the expression. Guided Practice for Examples 1, 2, and 3 Simplify the expression. 1. 8 ANSWER 2 2. 27 ANSWER 3 3. 75 ANSWER 5 3 4. 2 • 6 ANSWER 2 3 5. • 3 6 ANSWER 3 2

Simplify the expression. Guided Practice for Examples 1, 2, and 3 Simplify the expression. 6. • 12 8 ANSWER 4 6 7. WHAT IF? In Example 2, suppose that the person’s leg length is 26 inches. Use the simplified radical expression to approximate the person’s maximum walking speed. ANSWER 100 in. per sec