EXAMPLE
4
Use a Radical Model
You and a friend are working on a schooner. The distance d (in miles)
you can see to the horizon can be modeled by the equation
SAILING
d⫽
3h
ᎏ
冪莦
2
where h is your eye-level height (in feet) above the water. Your eye-level height
is 32 feet and your friend’s eye-level height is 18 feet. Write an expression that
shows how much farther you can see than your friend. Simplify the expression.
—————
—————
——————
32 ft
—————
——————
—————
——————
18 ft
—————
——————
—————
——
——————
——
Not drawn to scale
Solution
VERBAL
MODEL
LABELS
Difference
⫽ Your ⫺ Your friend’s
in distances
distance
distance
Difference in distances ⫽ D
Your distance ⫽
3(32)
ᎏ
冪莦
2
Your friend’s distance ⫽
ALGEBRAIC
MODEL
ANSWER 䊳
D ⫽
(miles)
3(32)
3(18)
ᎏ ⫺ 冪莦
ᎏ
冪莦
2
2
(miles)
3(18)
ᎏ
冪莦
2
(miles)
Write algebraic model.
D ⫽ 兹4苶8苶 ⫺ 兹2苶7苶
Simplify.
D ⫽ 兹1苶6苶苶p苶3 ⫺ 兹9苶苶p苶3
Factor using perfect square factors.
D ⫽ 4兹3苶 ⫺ 3兹3苶
Use product property and simplify.
D ⫽ 兹3苶 ⬇ 1.7
Subtract like radicals.
You can see about 1.7 miles farther than your friend.
Use a Radical Model
14. Your eye-level height is 16 feet and your friend’s eye-level height is 20 feet.
Write an expression showing how much farther your friend can see than you.
700
Chapter 12
Radicals and More Connections to Geometry