rite a number whose principal square root and cube root are both integers, 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.

Pages 422 and 417 attached 7-3
Square Root Functions
and Inequalities
Main Ideas
• Graph and analyze
square root functions.
• Graph square root
inequalities.
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 = 8d2,
where d is the diameter of the
cable in inches and w is the
weight in tons.
New Vocabulary
square root function
square root inequality
If you need to know what
diameter a steel cable should
have to support a given weight,
you can use the equation
d=
d = V
Square Root Functions If a function contains a square root of a variable,
it is called a square root function. The parent function of the family of
square root functions is y = Vx. The inverse of a atic function is a
square root function only if the range is restricted to nonnegative
numbers.
у
y = x2
y = x2
0
= +Vx
y = +Vx is not a function.
y = VX is a function.
In order for a square root to be a real number, the radicand cannot be
negative. When graphing a square root function, determine when the
radicand would be negative and exclude those values from the domain.
Lesson 7-3 Square Root Functions and Inequalities 397
Raymond Gehman/CORBIS
7-4
nth Roots
GET READY for the Lesson
Main Ideas
• Simplify radicals
• Use a calculator to
=
approximate radicals
The radius r of a sphere with volume V can be
3V
found using the formula r = This is an
example of an equation that contains an nth root.
In this case, n = 3.
New Vocabulary
nth root
principal root
Simplify Radicals Finding the square root of a number and squaring a
number are inverse operations. To find the square root of a number n,
you must find a number whose square is n.
Study Tip
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.
Look Back
Review square roots
in Lesson 5-4.
Powers
Factors
Roots
a? = 125
5.5.5 = 125
5 is a cube root of 125.
3 is a fourth root of 81.
a4 = 81
a = 32
3.3.3.3 = 81
2.2.2.2.2 = 32
2 is a fifth root of 32.
a = b
0.0.0.0…..q=b
n factors of a
a is an nth root of b.
This pattern suggests the following formal definition of an nth root.
KEY CONCEPT
Definition of nth Root
Word
For any real numbers a and b, and any positive integer n, if a” = b,
then a is an nth root of b.
Example Since 25 = 32, 2 is a fifth root of 32.
The symbol v indicates an nth root.
radical sign
index
V50
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 36, the radical sign indicates the principal square root. The
symbol Vb stands for the principal nth root of b. If n is odd and b is
negative, there will be no nonnegative root. In this case, the principal
root is negative.