1. 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

2. 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 l 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

3. 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.

4. 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

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

6. 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