Beginning and Intermediate Algebra

Margaret L. Lial , John Hornsby

Chapter 10

Roots, Radicals, and Root Functions - all with Video Answers

Educators

Section 1

Radical Expressions and Graphs

Problem 1

Decide whether each statement is true or false. If false, tell why.
Every positive number has two real square roots.

Melissa Stefan

Melissa Stefan

Numerade Educator

Problem 2

Decide whether each statement is true or false. If false, tell why.
A negative number has negative real square roots.

Melissa Stefan

Numerade Educator

Problem 3

Decide whether each statement is true or false. If false, tell why.
Every nonnegative number has two real
square roots.

Melissa Stefan

Numerade Educator

Problem 4

Decide whether each statement is true or false. If false, tell why.
The positive square root of a positive number is its principal square root.

Melissa Stefan

Numerade Educator

Problem 5

Decide whether each statement is true or false. If false, tell why.
The cube root of every nonzero real number has the same sign as the number itself.

Melissa Stefan

Numerade Educator

Problem 6

Decide whether each statement is true or false. If false, tell why.
Every positive number has three real cube roots.

Melissa Stefan

Numerade Educator

Problem 7

Find all square roots of each number. See Example 1.
$$
9
$$

Amy Jiang

Numerade Educator

Problem 8

Find all square roots of each number. See Example 1.
$$
16
$$

Amy Jiang

Numerade Educator

Problem 9

Find all square roots of each number. See Example 1.
$$
64
$$

Amy Jiang

Numerade Educator

Problem 10

Find all square roots of each number. See Example 1.
$$
100
$$

Melissa Stefan

Numerade Educator

Problem 11

Find all square roots of each number. See Example 1.
$$
169
$$

Melissa Stefan

Numerade Educator

Problem 12

Find all square roots of each number. See Example 1.
$$
225
$$

Melissa Stefan

Numerade Educator

Problem 13

Find all square roots of each number. See Example 1.
$$
\frac{25}{196}
$$

Melissa Stefan

Numerade Educator

Problem 14

Find all square roots of each number. See Example 1.
$$
\frac{81}{400}
$$

Melissa Stefan

Numerade Educator

Problem 15

Find all square roots of each number. See Example 1.
$$
900
$$

Melissa Stefan

Numerade Educator

Problem 16

Find all square roots of each number. See Example 1.
$$
1600
$$

Melissa Stefan

Numerade Educator

Problem 17

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{1}
$$

Melissa Stefan

Numerade Educator

Problem 18

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{4}
$$

Melissa Stefan

Numerade Educator

Problem 19

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{49}
$$

Melissa Stefan

Numerade Educator

Problem 20

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{81}
$$

Melissa Stefan

Numerade Educator

Problem 21

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{256}
$$

Melissa Stefan

Numerade Educator

Problem 22

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{196}
$$

Melissa Stefan

Numerade Educator

Problem 23

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{\frac{144}{121}}
$$

Melissa Stefan

Numerade Educator

Problem 24

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{\frac{49}{36}}
$$

Melissa Stefan

Numerade Educator

Problem 25

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{0.64}
$$

Melissa Stefan

Numerade Educator

Problem 26

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{0.16}
$$

Melissa Stefan

Numerade Educator

Problem 27

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{-121}
$$

Melissa Stefan

Numerade Educator

Problem 28

Find each square root. See Examples 2 and 4(c).
$$
\sqrt{-64}
$$

Melissa Stefan

Numerade Educator

Problem 29

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{-49}
$$

Melissa Stefan

Numerade Educator

Problem 30

Find each square root. See Examples 2 and 4(c).
$$
-\sqrt{-100}
$$

Melissa Stefan

Numerade Educator

Problem 31

Find the square of each radical expression. See Example 3.
$$
\sqrt{19}
$$

Melissa Stefan

Numerade Educator

Problem 32

Find the square of each radical expression. See Example 3.
$$
\sqrt{59}
$$

Melissa Stefan

Numerade Educator

Problem 33

Find the square of each radical expression. See Example 3.
$$
-\sqrt{19}
$$

Melissa Stefan

Numerade Educator

Problem 34

Find the square of each radical expression. See Example 3.
$$
-\sqrt{59}
$$

Melissa Stefan

Numerade Educator

Problem 35

Find the square of each radical expression. See Example 3.
$$
\sqrt{\frac{2}{3}}
$$

Melissa Stefan

Numerade Educator

Problem 36

Find the square of each radical expression. See Example 3.
$$
\sqrt{\frac{5}{7}}
$$

Melissa Stefan

Numerade Educator

Problem 37

Find the square of each radical expression. See Example 3.
$$
\sqrt{3 x^{2}+4}
$$

Melissa Stefan

Numerade Educator

Problem 38

Find the square of each radical expression. See Example 3.
$$
\sqrt{9 y^{2}+3}
$$

Melissa Stefan

Numerade Educator

Problem 39

What must be true about the variable a for each statement to be true?
$\sqrt{a}$ represents a positive number.

Melissa Stefan

Numerade Educator

Problem 40

What must be true about the variable a for each statement to be true?
$-\sqrt{a}$ represents a negative number.

Melissa Stefan

Numerade Educator

Problem 41

What must be true about the variable a for each statement to be true?
$\sqrt{a}$ is not a real number.

Melissa Stefan

Numerade Educator

Problem 42

What must be true about the variable a for each statement to be true?
$-\sqrt{a}$ is not a real number.

Melissa Stefan

Numerade Educator

Problem 43

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{25}
$$

Amy Jiang

Numerade Educator

Problem 44

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{169}
$$

Amy Jiang

Numerade Educator

Problem 45

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{29}
$$

Amy Jiang

Numerade Educator

Problem 46

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{33}
$$

Amy Jiang

Numerade Educator

Problem 47

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
-\sqrt{64}
$$

Amy Jiang

Numerade Educator

Problem 48

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
-\sqrt{81}
$$

Amy Jiang

Numerade Educator

Problem 49

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
-\sqrt{300}
$$

Amy Jiang

Numerade Educator

Problem 50

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
-\sqrt{500}
$$

Amy Jiang

Numerade Educator

Problem 51

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{-29}
$$

Amy Jiang

Numerade Educator

Problem 52

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{-47}
$$

Amy Jiang

Numerade Educator

Problem 53

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{1200}
$$

Amy Jiang

Numerade Educator

Problem 54

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 10.
$$
\sqrt{1500}
$$

Amy Jiang

Numerade Educator

Problem 55

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{94}
$$

Amy Jiang

Numerade Educator

Problem 56

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{43}
$$

Amy Jiang

Numerade Educator

Problem 57

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{51}
$$

Amy Jiang

Numerade Educator

Problem 58

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{30}
$$

Amy Jiang

Numerade Educator

Problem 59

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
-\sqrt{40}
$$

Amy Jiang

Numerade Educator

Problem 60

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
-\sqrt{63}
$$

Amy Jiang

Numerade Educator

Problem 61

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{23.2}
$$

Amy Jiang

Numerade Educator

Problem 62

Without using a calculator, determine between which two consecutive integers each square root lies. For example,
$\sqrt{75}$ is between 8 and $9,$ because $\sqrt{64}=8, \sqrt{81}=9,$ and $64<75<81$
$$
\sqrt{10.3}
$$

Amy Jiang

Numerade Educator

Problem 63

To help find cube roots, complete this list of perfect cubes.
$$1^{3}=\quad 2^{3}=\quad 3^{3}=\quad 4^{3}=\quad 5^{3}=$$
$$6^{3}=\quad 7^{3}=\quad 8^{3}=\quad 9^{3}=\quad 10^{3}=$$

Amy Jiang

Numerade Educator

Problem 64

To help find fourth roots, complete this list of perfect fourth powers.
$$1^{4}=\quad 2^{4}=\quad 3^{4}=\quad 4^{4}=\quad 5^{4}=$$
$$6^{4}=\quad 7^{4}=\quad 8^{4}=\quad 9^{4}=\quad 10^{4}=$$

Amy Jiang

Numerade Educator

Problem 65

Match each expression from Column I with the equivalent choice from Column II. Answers may be used more than once. See Examples 5 and 6.
I
(a) $-\sqrt{25}$
(b) $\sqrt{-25}$
(c) $\sqrt[3]{-27}$
(d) $\sqrt[5]{-32}$
(e) $\sqrt[4]{81}$
(f) $\sqrt[3]{8}$
II
A.) 3
B.)-2
C.)2
D.)-3
E.)-5
F.)Not a real number

Amy Jiang

Numerade Educator

Problem 66

Consider the expression $-\sqrt{-a} .$ Decide whether it is positive, negative, $0,$ or not a real number if
(a) $a>0$
(b) $a<0$
(c) $a=0$

Amy Jiang

Numerade Educator

Problem 67

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt{81}
$$

Amy Jiang

Numerade Educator

Problem 68

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt{121}
$$

Amy Jiang

Numerade Educator

Problem 69

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{216}
$$

Amy Jiang

Numerade Educator

Problem 70

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{343}
$$

Amy Jiang

Numerade Educator

Problem 71

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{-64}
$$

Amy Jiang

Numerade Educator

Problem 72

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{-125}
$$

Amy Jiang

Numerade Educator

Problem 73

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[3]{512}
$$

Amy Jiang

Numerade Educator

Problem 74

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[3]{1000}
$$

Amy Jiang

Numerade Educator

Problem 75

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[4]{1296}
$$

Amy Jiang

Numerade Educator

Problem 76

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[4]{625}
$$

Amy Jiang

Numerade Educator

Problem 77

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[4]{16}
$$

Amy Jiang

Numerade Educator

Problem 78

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[4]{256}
$$

Amy Jiang

Numerade Educator

Problem 79

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[4]{-625}
$$

Amy Jiang

Numerade Educator

Problem 80

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[4]{-256}
$$

Amy Jiang

Numerade Educator

Problem 81

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[6]{64}
$$

Amy Jiang

Numerade Educator

Problem 82

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[6]{729}
$$

Amy Jiang

Numerade Educator

Problem 83

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[6]{-32}
$$

Amy Jiang

Numerade Educator

Problem 84

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[8]{-1}
$$

Amy Jiang

Numerade Educator

Problem 85

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt{\frac{64}{81}}
$$

Amy Jiang

Numerade Educator

Problem 86

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt{\frac{100}{9}}
$$

Amy Jiang

Numerade Educator

Problem 87

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{\frac{64}{27}}
$$

Amy Jiang

Numerade Educator

Problem 88

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[4]{\frac{81}{16}}
$$

Amy Jiang

Numerade Educator

Problem 89

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[6]{\frac{1}{64}}
$$

Amy Jiang

Numerade Educator

Problem 90

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[5]{\frac{1}{32}}
$$

Amy Jiang

Numerade Educator

Problem 91

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[3]{-27}
$$

Amy Jiang

Numerade Educator

Problem 92

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt[3]{-64}
$$

Amy Jiang

Numerade Educator

Problem 93

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt{0.25}
$$

Amy Jiang

Numerade Educator

Problem 94

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt{0.36}
$$

Amy Jiang

Numerade Educator

Problem 95

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt{0.49}
$$

Amy Jiang

Numerade Educator

Problem 96

Find each root that is a real number. See Examples 5 and 6.
$$
-\sqrt{0.81}
$$

Amy Jiang

Numerade Educator

Problem 97

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{0.001}
$$

Amy Jiang

Numerade Educator

Problem 98

Find each root that is a real number. See Examples 5 and 6.
$$
\sqrt[3]{0.125}
$$

Amy Jiang

Numerade Educator

Problem 99

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt{x+3}
$$

Tony Ni

Numerade Educator

Problem 100

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt{x-5}
$$

Amy Jiang

Numerade Educator

Problem 101

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt{x}-2
$$

Amy Jiang

Numerade Educator

Problem 102

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt{x}+4
$$

Amy Jiang

Numerade Educator

Problem 103

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt[3]{x}-3
$$

Tony Ni

Numerade Educator

Problem 104

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt[3]{x}+1
$$

Amy Jiang

Numerade Educator

Problem 105

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt[3]{x-3}
$$

Tony Ni

Numerade Educator

Problem 106

Graph each function and give its domain and range. See Example 7.
$$
f(x)=\sqrt[3]{x+1}
$$

Amy Jiang

Numerade Educator

Problem 107

Simplify each root. See Examples 8 and 9.
$$
\sqrt{12^{2}}
$$

Amy Jiang

Numerade Educator

Problem 108

Simplify each root. See Examples 8 and 9.
$$
\sqrt{19^{2}}
$$

Amy Jiang

Numerade Educator

Problem 109

Simplify each root. See Examples 8 and 9.
$$
\sqrt{(-10)^{2}}
$$

Amy Jiang

Numerade Educator

Problem 110

Simplify each root. See Examples 8 and 9.
$$
\sqrt{(-13)^{2}}
$$

Amy Jiang

Numerade Educator

Problem 111

Simplify each root. See Examples 8 and 9.
$$
\sqrt[6]{(-2)^{6}}
$$

Amy Jiang

Numerade Educator

Problem 112

Simplify each root. See Examples 8 and 9.
$$
\sqrt[6]{(-4)^{6}}
$$

Amy Jiang

Numerade Educator

Problem 113

Simplify each root. See Examples 8 and 9.
$$
\sqrt[5]{(-9)^{5}}
$$

Amy Jiang

Numerade Educator

Problem 114

Simplify each root. See Examples 8 and 9.
$$
\sqrt[5]{(-8)^{5}}
$$

Amy Jiang

Numerade Educator

Problem 115

Simplify each root. See Examples 8 and 9.
$$
-\sqrt[6]{(-5)^{6}}
$$

Amy Jiang

Numerade Educator

Problem 116

Simplify each root. See Examples 8 and 9.
$$
-\sqrt[6]{(-7)^{6}}
$$

Amy Jiang

Numerade Educator

Problem 117

Simplify each root. See Examples 8 and 9.
$$
\sqrt{x^{2}}
$$

Amy Jiang

Numerade Educator

Problem 118

Simplify each root. See Examples 8 and 9.
$$
-\sqrt{x^{2}}
$$

Amy Jiang

Numerade Educator

Problem 119

Simplify each root. See Examples 8 and 9.
$$
\sqrt{(-z)^{2}}
$$

Amy Jiang

Numerade Educator

Problem 120

Simplify each root. See Examples 8 and 9.
$$
\sqrt{(-q)^{2}}
$$

Amy Jiang

Numerade Educator

Problem 121

Simplify each root. See Examples 8 and 9.
$$
\sqrt[3]{x^{3}}
$$

Amy Jiang

Numerade Educator

Problem 122

Simplify each root. See Examples 8 and 9.
$$
-\sqrt[3]{x^{3}}
$$

Amy Jiang

Numerade Educator

Problem 123

Simplify each root. See Examples 8 and 9.
$$
\sqrt[3]{x^{15}}
$$

Amy Jiang

Numerade Educator

Problem 124

Simplify each root. See Examples 8 and 9.
$$
\sqrt[3]{m^{9}}
$$

Amy Jiang

Numerade Educator

Problem 125

Simplify each root. See Examples 8 and 9.
$$
\sqrt[6]{x^{30}}
$$

Amy Jiang

Numerade Educator

Problem 126

Simplify each root. See Examples 8 and 9.
$$
\sqrt[4]{k^{20}}
$$

Amy Jiang

Numerade Educator

Problem 127

Choose the closest approximation of each square root.
$\sqrt{123.5}$
$\begin{array}{llll}{\text { A. } 9} & {\text { B. } 10} & {\text { C. } 11}\end{array}$D. 12

Amy Jiang

Numerade Educator

Problem 128

Choose the closest approximation of each square root.
$$
\begin{aligned}
&\sqrt{67.8}\\
&\begin{array}{lllll}
{\text { A. } 7} & {\text { B. } 8} & {\text { C. } 9} & {\text { D. } 10}
\end{array}
\end{aligned}
$$

Amy Jiang

Numerade Educator

Problem 129

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt{9483}
$$

Amy Jiang

Numerade Educator

Problem 130

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt{6825}
$$

Amy Jiang

Numerade Educator

Problem 131

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt{284.361}
$$

Amy Jiang

Numerade Educator

Problem 132

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt{846.104}
$$

Amy Jiang

Numerade Educator

Problem 133

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
-\sqrt{82}
$$

Amy Jiang

Numerade Educator

Problem 134

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
-\sqrt{91}
$$

Amy Jiang

Numerade Educator

Problem 135

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[3]{423}
$$

Amy Jiang

Numerade Educator

Problem 136

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[3]{555}
$$

Amy Jiang

Numerade Educator

Problem 137

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[4]{100}
$$

Amy Jiang

Numerade Educator

Problem 138

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[4]{250}
$$

Amy Jiang

Numerade Educator

Problem 139

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[5]{23.8}
$$

Amy Jiang

Numerade Educator

Problem 140

Find a decimal approximation for each radical. Round the answer to three decimal places.
See Example 10.
$$
\sqrt[5]{98.4}
$$

Amy Jiang

Numerade Educator

Problem 141

Refer to the rectangle to answer the questions in Exercises 141 and 142.
Which one of the following is the best estimate of its area?
A. 50
B. 250
C. 2500
D. 100
CAN'T COPY THE FIGURE

Amy Jiang

Numerade Educator

Problem 142

Refer to the rectangle to answer the questions in Exercises 141 and 142.
Which one of the following is the best estimate of its perimeter?
A. 15
B. 250
C. 100
D. 30
CAN'T COPY THE FIGURE

Amy Jiang

Numerade Educator

Problem 143

Solve each problem. See Example 11.
Use the formula in Example 11 to calculate the resonant frequency of a circuit to the nearest thousand if $L=7.237 \times 10^{-5}$ henry and $C=2.5 \times 10^{-10}$ farad.

Amy Jiang

Numerade Educator

Problem 144

Solve each problem. See Example 11.
The threshold weight $T$ for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged $40-49$ is related to height $h$ in inches by the formula
$$
h=12.3 \sqrt[3]{T}
$$
What height corresponds to a threshold weight of 216 Ib for a 43 -year-old man? Round your answer to the nearest inch and then to the nearest tenth of a foot.

Amy Jiang

Numerade Educator

Problem 145

Solve each problem. See Example 11.
According to an article in The World Scanner Report, the distance $D,$ in miles, to the horizon from an observer's point of view over water or "flat" earth is given by
$$
D=\sqrt{2 H}
$$
where $H$ is the height of the point of view, in feet. If a person whose cyes are 6 ft above ground level is standing at the top of a hill 44 ft above "flat" earth, approximately how far to the horizon will she be able to see?
CAN'T COPY THE IMAGE

Amy Jiang

Numerade Educator

Problem 146

Solve each problem. See Example 11.
The time $t$ in seconds for one complete swing of a simple pendulum, where $L$ is the length of the pendulum in feet, and $g$, the acceleration due to gravity, is about 32 ft per $\sec ^{2},$ is
$x+2 \sqrt{\frac{x}{x}}$
Find the time of a complete swing of a 2 -ft pendulum to the nearest tenth of a second..

Amy Jiang

Numerade Educator

Problem 147

Solve each problem. See Example 11.
Heron's formula gives a method of finding the area of a triangle if the lengths of its sides are known. Suppose that $a, b,$ and $c$ are the lengths of the sides. Let $s$ denote onenalf of the perimeter of the triangle (called the semiperimeter); that is, $s=\frac{1}{2}(a+b+c) .$ Then the area of the triangle is
$$
\mathscr{A}=\sqrt{s(s-a)(s-b)(s-c)}
$$
Find the area of the Bermuda Triangle, to the nearest thousand square miles, if the "sides" of this triangle measure approximately $850 \mathrm{mi}, 925 \mathrm{mi}$, and $1300 \mathrm{mi}$.

Aman Gupta

Numerade Educator

Problem 148

Solve each problem. See Example 11.
Use Heron's formula from Exercise 147 to find the area of a triangle with sides of lengths $a=11 \mathrm{m}, b=60 \mathrm{m},$ and $c=61 \mathrm{m}$

Amy Jiang

Numerade Educator

Problem 149

Solve each problem. See Example 11.
The coefficient of self-induction $L$ (in henrys), the energy $P$ stored in an electronic circuit (in joules), and the current $I$ (in amps) are related by this formula. $I=\sqrt{\frac{2 P}{L}}$
(a) Find $I$ if $P=120$ and $L=80$
(b) Find $I$ if $P=100$ and $L=40$

Amy Jiang

Numerade Educator

Problem 150

Solve each problem. See Example 11.
The Vietnam Veterans Memorial in Washington, DC, in the shape of an unenclosed isosceles triangle with equal sides of length 246.75 ft. If the triangle were enclosed, the third side would have length 438.14 ft. Use Heron's formula from Exercise 147 to find the area of this enclosure to the nearest hundred square feet. (Source: Information pamphlet obtained at the Vietnam Veterans Memorial.)
CAN'T COPY THE IMAGE

Amy Jiang

Numerade Educator

Problem 151

Apply the rules for exponents. Write each result with only positive exponents. Assume that all variables represent nonzero real numbers. See Sections 4.1 and 4.2.
$$
x^{5} \cdot x^{-1} \cdot x^{-3}
$$

Amy Jiang

Numerade Educator

Problem 152

Apply the rules for exponents. Write each result with only positive exponents. Assume that all variables represent nonzero real numbers. See Sections 4.1 and 4.2.
$$
\left(4 x^{2} y^{3}\right)\left(2^{3} x^{5} y\right)
$$

Amy Jiang

Numerade Educator

Problem 153

Apply the rules for exponents. Write each result with only positive exponents. Assume that all variables represent nonzero real numbers. See Sections 4.1 and 4.2.
$$
\left(\frac{2}{3}\right)^{-3}
$$

Amy Jiang

Numerade Educator

Problem 154

Apply the rules for exponents. Write each result with only positive exponents. Assume that all variables represent nonzero real numbers. See Sections 4.1 and 4.2.
$$
\frac{5}{5^{-1}}
$$

Amy Jiang

Numerade Educator