Intermediate Algebra (11th edition)

The windchill factoris a measure of the cooling effect that the wind has on a person’s skin. It

calculates the equivalent cooling temperature if there were no wind. The National Weather

Service uses the formula

where T is the temperature in °F and V is the wind speed in miles per hour, to calculate wind-

chill. The chart gives the windchill factor for various wind speeds and temperatures at which

frostbite is a risk, and how quickly it may occur.

Windchill temperature=35.74+0.6215T-35.75V4/25+0.4275TV4/25,

SECTION 8.3 Simplifying Radical Expressions 443

Calm 40 30 20 10 0 –10 –20 –30 –40

5 36 25 13 1 –11 –22 –34 –46 –57

10 34 21 9 –4 –16 –28 –41 –53 –66

15 32 19 6 –7 –19 –32 –45 –58 –71

20 30 17 4 –9 –22 –35 –48 –61 –74

25 29 16 3 –11 –24 –37 –51 –64 –78

30 28 15 1 –12 –26 –39 –53 –67 –80

35 28 14 0 –14 –27 –41 –55 –69 –82

40 27 13 –1 –15 –29 –43 –57 –71 –84

Wind speed (mph)

Temperature (F)

Source: National Oceanic and Atmospheric Administration, National Weather Service.

Frostbites times: 30 minutes 10 minutes 5 minutes

0 3 55 99 3 5 71 84

inutes

8

Use the formula and a calculator to determine the windchill to the nearest tenth of a degree,

given the following conditions. Compare your answers with the appropriate entries in the table.

107. 15-mph wind 108. 30-mph wind
     109.20°F, 20-mph wind 110.40°F, 10-mph wind

30°F, 10°F,

Simplify each pair of expressions, and then compare the results. See Section 8.1.

111. 112.

B

3

27

729

2327

23729

225 # 236 , 225 # 36 ,

PREVIEW EXERCISES

OBJECTIVES

Simplifying Radical Expressions

8.3

1 Use the product
rule for radicals.

2 Use the quotient
rule for radicals.

3 Simplify radicals.

4 Simplify products
and quotients of
radicals with
different indexes.

5 Use the Pythagorean
theorem.

6 Use the distance
formula.

OBJECTIVE 1 Use the product rule for radicals.Consider the expressions

and. Are they equal?

The result is the same.

This is an example of the product rule for radicals.

236 # 24 = 6 # 2 = 12

236 # 4 = 2144 = 12

236 # 4 236 # 24

Product Rule for Radicals

If and are real numbers and nis a natural number, then

That is, the product of two nth roots is the nth root of the product.

n

2 a#

n

2 b

n

2 ab.

2

n

2 b

n

a