Example 1 Simplifying Radical Expressions

Write the radical expression in simplest form.

a. 250 b. 108

= 5 10 Simplify.

Factor out greatest perfect square factor.b. 108 = 36 • 3

= 36 • 3 Product property of square roots

= 25 • Product property of square roots 10

3= Simplify.6

Factor out greatest perfect square factor.

SOLUTION

a. 250 = 25 • 10

Example 2 Using a Radical Expression in Real Life

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).

WALKING SPEED

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 Using a Radical Expression in Real Life

= 64 • 6l Product property of square roots

= 6l Simplify.8

ANSWER In simplest form, 384l = 6l8

106 Approximate using a calculator.≈

b. 6l8 Substitute 29 for l.= 6 • 298

= 174 Multiply.8

ANSWER

The person’s maximum walking speed is approximately 106 inches per second.

Example 3 Simplifying a Product of Two Radicals

= 25 • 2 Factor out greatest perfect square factor.

= 25 • Product property of square roots 2

= 2 Simplify.5

5 • 10 = 50 Product property of square roots

Simplify the radical expression 5 • 10.

Guided Practice

Simplify the expression.

for Examples 1, 2, and 3

1. 8

ANSWER 3 32. 27

ANSWER 5 33. 75

ANSWER 2 34. 2 • 6

ANSWER 3 2

ANSWER 2 2

5. •3 6

Guided Practice for Examples 1, 2, and 3

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

ANSWER 4 6

Simplify the expression.

6. • 128