Radical Functions, algebra homework help

1. OPEN ENDED Write a number whose principal square root and cube root are both integers.
2. Writing in Math Refer to the information on page 422 to explain how the nth roots apply to geometry. Analyze what happens to the value of r as the value of V increases.
3. Writing in Math Refer to the information on page 417 to explain how square root functions can be used in bridge design. Assess the weights for which a diameter less than 1 is reasonable. Evaluate the amount of weight that the Sunshine Skyway Bridge can support.

422
4
nth Roots
GET READY for the Lesson
5
lator to
e radicals
The radius r of a sphere with volume V can be
found using the formula r = This is an
example of an equation that contains an nth root
In this case, n-3.
bulary
Simplify Radicals Finding the square root of a number and squaring a
number are inverse operations. To find the square root of a number a,
you must find a number whose square is w.
Similarly, the inverse of raising a number to the nth power is finding the
nth root of a number. The table below shows the relationship between
raising a number to a power and taking that root of a number.
y Tip
ack
are roots
54.
Powers
Factors
5.55 – 125
3 SS HI
2-2-2-2-2 = 32
81
G= 32
Roots
5 is a obra nowo of 125
Slourth rout of HI
2 s a fifth root of 32
00
ab
Hab
consola
a ban nth root of b.
This pattern suggests the following formal definition of an nth root.
KEY CONCEPT
Definition of nth Root
Merd For any real numbers a and b, and any positive integer n, if on-b,
then a is an nth root of b.
Excmyle Since 25 = 32, 2 is a fifth root of 32.
The symbol indicates an ath root.
radical sign
index
150
radicand
Some numbers have more than one real nth root. For example, 36 has
two square roots, 6 and -6. When there is more than one real root, the
nonnegative root is called the principal root. When no index is given, as
in V36, the radical sign indicates the principal square root. The
symbol Vb stands for the principal nth root of b. If n is odd and bis
negative, there will be no nonnegative root. In this case, the principal
root is negative.
D2 Chapter 7 Radical Equations and inequalities
15,320
AUG
24
a
Square Root Functions
and Inequalities
Q
GET READY for the Lesson
The Sunshine Skyway Bridge
across Tampa Bay, Florida, is
supported by 21 steel cables, each
9 inches in diameter. The amount
of weight that a steel cable can
support is given by w – 812,
where is the diameter of the
cable in inches and w is the
weight in tons.
If you need to know what
diameter a steel cable should
have to support a given weight,
you can use the equation
TO
Square Root Functions If a function contains a square foot of a variable,
it is called a square root function. The parent function of the family of
square root functions is y= V1. The inverse of a quadratic function is a
square root function only if the range is restricted to nonnegative
numbers.
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