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Intermediate Algebra for College Students

Allen R. Angel; Dennis C. Runde

Chapter 7

Roots, Radicals, and Complex Numbers - all with Video Answers

Educators

Section 1

Roots and Radicals

00:23

Problem 1

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
The symbol $\sqrt{\text { }}$ is called the ____ sign.

Matt Gibson
Matt Gibson
Numerade Educator
00:19

Problem 2

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
In the radical expression $\sqrt[3]{5}$ the 3 is the ____.

AG
Ankit Gupta
Numerade Educator
00:19

Problem 3

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
In the radical expression $\sqrt[3]{5}$ the 5 is the ____.

AG
Ankit Gupta
Numerade Educator
00:14

Problem 4

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
When we say " ______ root" we refer to a radical expression with an index of 2 .

Lily An
Lily An
Numerade Educator
00:14

Problem 5

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
When we say " ______ root" we refer to a radical expression with an index of 3 .

Lily An
Lily An
Numerade Educator
00:15

Problem 6

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
The _________ square root of $a$, written $\sqrt{a}$, is the positive number $b$ such that $b^{2}=a$.

AG
Ankit Gupta
Numerade Educator
00:23

Problem 7

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
The ______ square root of $a$, written $-\sqrt{a}$, is the opposite of the principal square root of $a$.

Matt Gibson
Matt Gibson
Numerade Educator
00:13

Problem 8

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
A _______ number can be written as either a terminating or a repeating decimal number.

AG
Ankit Gupta
Numerade Educator
00:23

Problem 9

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
The ______ root of a negative number is not a real number.

Matt Gibson
Matt Gibson
Numerade Educator
00:23

Problem 10

Fill in the blanks with the appropriate word, phrase, or symbol(s) from the following list.
$$\begin{array}{lllllr}\text { odd } & \text { index } & \text { principal } & \text { cube } & \text { rational } & \text { radical } \\\text { square } & \text { radicand } & \text { even } & \text { irrational } & \text { negative }.\end{array}$$
The ______ root of a negative number is a negative number.

Matt Gibson
Matt Gibson
Numerade Educator
00:08

Problem 11

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
a) $\sqrt{25}$
b) $-\sqrt{25}$
c) $\sqrt{-25}$
d) $-\sqrt{-25}$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
04:27

Problem 12

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
a) $\sqrt{64}$
b) $-\sqrt{64}$
c) $\sqrt{-64}$
d) $-\sqrt{-64}$

Mihir Nayar
Mihir Nayar
Numerade Educator
00:31

Problem 13

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
a) $\sqrt[3]{8}$
b) $-\sqrt[3]{8}$
c) $\sqrt[3]{-8}$
d) $-\sqrt[3]{-8}$

Lily An
Lily An
Numerade Educator
02:53

Problem 14

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
.a) $\sqrt[3]{27}$
b) $-\sqrt[3]{27}$
c) $\sqrt[3]{-27}$

Christina Shute
Christina Shute
Numerade Educator
01:46

Problem 15

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
a) $\sqrt[4]{16}$
b) $\sqrt[4]{-16}$
c) $-\sqrt[4]{16}$
d) $-\sqrt[4]{-16}$

Daniel Nolan
Daniel Nolan
Numerade Educator
00:31

Problem 16

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
a) $\sqrt[4]{625}$
b) $-\sqrt[4]{625}$
c) $\sqrt[4]{-625}$
d) $-\sqrt[4]{-625}$

Lily An
Lily An
Numerade Educator
01:13

Problem 17

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{-1}$

Julie Silva
Julie Silva
Numerade Educator
01:13

Problem 18

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[5]{-1}$

Julie Silva
Julie Silva
Numerade Educator
01:13

Problem 19

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[4]{-1}$

Julie Silva
Julie Silva
Numerade Educator
01:13

Problem 20

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[6]{-1}$

Julie Silva
Julie Silva
Numerade Educator
00:31

Problem 21

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{-64}$

Natalie Anderson
Natalie Anderson
Numerade Educator
01:00

Problem 22

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{-216}$

Julie Silva
Julie Silva
Numerade Educator
01:36

Problem 23

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[5]{32}$

Narayan Hari
Narayan Hari
Numerade Educator
00:31

Problem 24

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[6]{64}$

Natalie Anderson
Natalie Anderson
Numerade Educator
00:37

Problem 25

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt{\frac{25}{81}}$

Natalie Anderson
Natalie Anderson
Numerade Educator
00:19

Problem 26

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt{\frac{49}{100}}$

Amy Jiang
Amy Jiang
Numerade Educator
01:01

Problem 27

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{-\frac{8}{125}}$

Julie Silva
Julie Silva
Numerade Educator
01:00

Problem 28

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
x$\sqrt[3]{-\frac{216}{1331}}$

Julie Silva
Julie Silva
Numerade Educator
00:38

Problem 29

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt{6.25}$

Tony Ni
Tony Ni
Numerade Educator
01:18

Problem 30

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt{10.24}$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 31

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{1.728}$

Julie Silva
Julie Silva
Numerade Educator
00:08

Problem 32

Evaluate each radical expression if it is a real number. If the expression is not a real number, so state.
$\sqrt[3]{15.625}$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:57

Problem 33

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt{3}$
b) $-\sqrt{7}$
c) $\sqrt{-13}$
d) $-\sqrt{-23}$

Victor Salazar
Victor Salazar
Numerade Educator
00:40

Problem 34

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt{-31}$
b) $-\sqrt{41}$
c) $-\sqrt{-53}$
d) $\sqrt{59}$

Erika Bustos
Erika Bustos
Numerade Educator
00:40

Problem 35

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt[3]{5}$
b) $-\sqrt[3]{11}$
c) $\sqrt[3]{-17}$
d) $-\sqrt[3]{-29}$

Erika Bustos
Erika Bustos
Numerade Educator
00:40

Problem 36

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt[3]{-37}$
b) $-\sqrt[3]{43}$
c) $-\sqrt[3]{-61}$
d) $\sqrt[3]{67}$

Erika Bustos
Erika Bustos
Numerade Educator
00:40

Problem 37

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt{17}$
b) $\sqrt{-17}$
c) $\sqrt[3]{17}$
d) $\sqrt[3]{-17}$

Erika Bustos
Erika Bustos
Numerade Educator
00:18

Problem 38

Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
a) $\sqrt{-101}$
b) $-\sqrt{101}$
c) $\sqrt[3]{-101}$
d) $-\sqrt[3]{-101}$

Amy Jiang
Amy Jiang
Numerade Educator
00:35

Problem 39

Use absolute value to evaluate.
$\sqrt{7^{2}}$

AG
Ankit Gupta
Numerade Educator
00:32

Problem 40

Use absolute value to evaluate.
$\sqrt{3^{2}}$

Krishna Kumar
Krishna Kumar
Numerade Educator
00:32

Problem 41

Use absolute value to evaluate.
$\sqrt{(-3)^{2}}$

Krishna Kumar
Krishna Kumar
Numerade Educator
00:35

Problem 42

Use absolute value to evaluate.
$\sqrt{(-7)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:35

Problem 43

Use absolute value to evaluate.
$\sqrt{119^{2}}$

AG
Ankit Gupta
Numerade Educator
00:35

Problem 44

Use absolute value to evaluate.
$\sqrt{(-119)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:31

Problem 45

Use absolute value to evaluate.
$\sqrt{(-2.78)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:31

Problem 46

Use absolute value to evaluate.
$\sqrt{(2.78)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:31

Problem 47

Use absolute value to evaluate.
$\sqrt{\left(-\frac{271}{311}\right)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:35

Problem 48

Use absolute value to evaluate.
$\sqrt{\left(\frac{217}{311}\right)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:31

Problem 49

Use absolute value to evaluate.
$\sqrt{\left(\frac{517}{711}\right)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:31

Problem 50

Use absolute value to evaluate.
$\sqrt{\left(-\frac{517}{711}\right)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:28

Problem 51

Write as an absolute value.
$\sqrt{(x-8)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:26

Problem 52

Write as an absolute value.
$\sqrt{(a+10)^{2}}$

AG
Ankit Gupta
Numerade Educator
00:30

Problem 53

Write as an absolute value.
$\sqrt{(5 x-11)^{2}}$

AG
Ankit Gupta
Numerade Educator
03:05

Problem 54

Write as an absolute value.
$\sqrt{(7 a-11 b)^{2}}$

Demi Nelson
Demi Nelson
Numerade Educator
00:19

Problem 55

Write as an absolute value.
$\sqrt{\left(3 x^{2}-1\right)^{2}}$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:00

Problem 56

Write as an absolute value.
$\sqrt{\left(7 y^{2}-3 y\right)^{2}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:23

Problem 57

Write as an absolute value.
$\sqrt{\left(6 a^{3}-5 b^{4}\right)^{2}}$

Vysakh M
Vysakh M
Numerade Educator
00:58

Problem 58

Write as an absolute value.
$\sqrt{\left(9 y^{4}-2 z^{3}\right)^{2}}$

Erika Bustos
Erika Bustos
Numerade Educator
00:24

Problem 59

Use absolute value to simplify. You may need to factor first.
$\sqrt{x^{10}}$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:04

Problem 60

Use absolute value to simplify. You may need to factor first.
$\sqrt{y^{22}}$

Erika Bustos
Erika Bustos
Numerade Educator
00:13

Problem 61

Use absolute value to simplify. You may need to factor first.
$\sqrt{w^{50}}$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:58

Problem 62

Use absolute value to simplify. You may need to factor first.
$\sqrt{z^{70}}$

Vysakh M
Vysakh M
Numerade Educator
01:02

Problem 63

Use absolute value to simplify. You may need to factor first.
$\sqrt{a^{2}-8 a+16}$

Erika Bustos
Erika Bustos
Numerade Educator
00:32

Problem 64

Use absolute value to simplify. You may need to factor first.
$\sqrt{x^{2}-12 x+36}$

Jeyasree R T
Jeyasree R T
Numerade Educator
00:58

Problem 65

Use absolute value to simplify. You may need to factor first.
$\sqrt{9 a^{2}+12 a b+4 b^{2}}$

Erika Bustos
Erika Bustos
Numerade Educator
01:04

Problem 66

Use absolute value to simplify. You may need to factor first.
$\sqrt{4 x^{2}+20 x y+25 y^{2}}$

Andrew John De Los Santos
Andrew John De Los Santos
Numerade Educator
00:34

Problem 67

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{25 a^{2}}$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:21

Problem 68

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{121 x^{6}}$

Nick Johnson
Nick Johnson
Numerade Educator
00:26

Problem 69

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{16 c^{6}}$

James Kiss
James Kiss
Numerade Educator
00:33

Problem 70

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{169 d^{10}}$

Nick Johnson
Nick Johnson
Numerade Educator
00:17

Problem 71

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{x^{2}+4 x+4}$

Erika Bustos
Erika Bustos
Numerade Educator
00:41

Problem 72

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{9 a^{2}-6 a+1}$

James Kiss
James Kiss
Numerade Educator
00:32

Problem 73

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{4 x^{2}+4 x y+y^{2}}$

Erika Bustos
Erika Bustos
Numerade Educator
00:49

Problem 74

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{16 b^{2}-40 b c+25 c^{2}}$

Amy Jiang
Amy Jiang
Numerade Educator
01:31

Problem 75

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$f(x)=\sqrt{5 x-6}, f(2)$

Erika Bustos
Erika Bustos
Numerade Educator
00:52

Problem 76

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$f(c)=\sqrt{7 c+1}, f(5)$

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 77

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$q(x)=\sqrt{76-3 x}, q(4)$

Melissa Stefan
Melissa Stefan
Numerade Educator
01:03

Problem 78

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$q(b)=\sqrt{9 b+34}, q(-1)$

Amy Jiang
Amy Jiang
Numerade Educator
00:52

Problem 79

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$f(x)=\sqrt{7 x-20}, f(1)$

Amy Jiang
Amy Jiang
Numerade Educator
00:39

Problem 80

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$g(x)=\sqrt{x^{2}-25}, g(-4)$

Amy Jiang
Amy Jiang
Numerade Educator
00:34

Problem 81

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$g(x)=\sqrt{64-8 x}, g(-3)$

Victor Salazar
Victor Salazar
Numerade Educator
00:52

Problem 82

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$f(a)=\sqrt{14 a-36}, f(4)$

Amy Jiang
Amy Jiang
Numerade Educator
00:49

Problem 83

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$h(t)=\sqrt[3]{3 t^{2}+5 t-16}, h(1)$

Tony Ni
Tony Ni
Numerade Educator
00:28

Problem 84

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$c(x)=\sqrt[3]{5 x^{2}-8 x-31}, c(2)$

Tony Ni
Tony Ni
Numerade Educator
03:11

Problem 85

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$s(t)=\sqrt[4]{t^{3}-t^{2}+t+40,} s(-3)$

Ben Thatcher
Ben Thatcher
Numerade Educator
01:37

Problem 86

For each function, determine the indicated value. Use a calculator to approximate each irrational number to the nearest hundredth. If the expression is not a real number, so state.
$t(x)=\sqrt[4]{2 x^{3}-3 x^{2}+6 x}, t(2)$

Amy Jiang
Amy Jiang
Numerade Educator
01:42

Problem 87

Determine $f(81)$ if $f(x)=x+\sqrt{x}+7$.

Dwijendra Rao
Dwijendra Rao
Numerade Educator
00:59

Problem 88

Determine $g(25)$ if $g(x)=x^{2}+\sqrt{x}-13$.

Melissa Salvador
Melissa Salvador
Numerade Educator
01:09

Problem 89

Determine $t(18)$ if $t(x)=\frac{x}{2}+\sqrt{2 x}-4$.

AG
Ankit Gupta
Numerade Educator
00:27

Problem 90

Determine $m(36)$ if $m(x)=\frac{x}{3}+\sqrt{4 x}+10$.

Amy Jiang
Amy Jiang
Numerade Educator
00:41

Problem 91

Determine $k(8)$ if $k(x)=x^{2}+\sqrt{\frac{x}{2}}-21$.

Amy Jiang
Amy Jiang
Numerade Educator
01:23

Problem 92

Determine $r(45)$ if $r(x)=\frac{x}{9}+\sqrt{\frac{x}{5}}+13$.

James Kiss
James Kiss
Numerade Educator
01:31

Problem 93

Select a value for $x$ for which $\sqrt{(2 x+1)^{2}} \neq 2 x+1$.

Ashley Jordon
Ashley Jordon
Numerade Educator
01:03

Problem 94

Select a value for $x$ for which $\sqrt{(5 x-3)^{2}} \neq 5 x-3$.

James Kiss
James Kiss
Numerade Educator
02:36

Problem 95

By considering the domains of the functions in Exercises 95 through 98 , match each function with its graph, labeled a) through d).
$f(x)=\sqrt{x}$
a.Graph Can`t Copy
b.Graph Can`t Copy

Kevin Harmer
Kevin Harmer
Numerade Educator
01:46

Problem 96

By considering the domains of the functions, match each function with its graph, labeled a) through d).
$f(x)=\sqrt{x^{2}}$
a.Graph Can`t Copy
b.Graph Can`t Copy
c.Graph Can`t Copy
d.Graph Can`t Copy

Carson Merrill
Carson Merrill
Numerade Educator
07:40

Problem 97

By considering the domains of the functions, match each function with its graph, labeled a) through d).
$f(x)=\sqrt{x-5}$
a.Graph Can`t Copy
b.Graph Can`t Copy
c.Graph Can`t Copy
d.Graph Can`t Copy

Eric Mockensturm
Eric Mockensturm
Numerade Educator
07:40

Problem 98

By considering the domains of the functions, match each function with its graph, labeled a) through d).
$f(x)=\sqrt{x+5}$
a.Graph Can`t Copy
b.Graph Can`t Copy
c.Graph Can`t Copy
d.Graph Can`t Copy

Eric Mockensturm
Eric Mockensturm
Numerade Educator
00:37

Problem 99

Graph $f(x)=\sqrt{x+1}$.

AG
Ankit Gupta
Numerade Educator
01:34

Problem 100

Graph $g(x)=-\sqrt{x}$.

Heather Zimmers
Heather Zimmers
Numerade Educator
01:34

Problem 101

Graph $g(x)=\sqrt{x}+1$.

Heather Zimmers
Heather Zimmers
Numerade Educator
02:08

Problem 102

Graph $f(x)=\sqrt{x-2}$.

AG
Ankit Gupta
Numerade Educator
00:43

Problem 103

Give a radical function whose domain is $\{x \mid x \geq 8\}$.

Joshua Eastwood
Joshua Eastwood
Numerade Educator
00:19

Problem 104

Give a radical function whose domain is $\{x \mid x \leq 5\}$.

Amy Jiang
Amy Jiang
Numerade Educator
01:43

Problem 105

The velocity, $V$, of an object, in feet per second, after it has fallen a distance, $h$, in feet, can be determined by the formula $V=\sqrt{64.4 h}$. A pile driver is a large mass that is used as a hammer to drive pilings into soft earth to support a building or other structure. With what velocity will the hammer hit the piling if it falls from
a) 20 feet above the top of the piling?
b) 40 feet above the top of the piling?

Breanna Ollech
Breanna Ollech
Numerade Educator
02:23

Problem 106

Scripps Institution of Oceanography in La Jolla, California, developed the formula for relating wind speed, $u$, in knots, with the height, $H$, in feet, of the waves the wind produces in certain areas of the ocean. This formula is
$$
u=\sqrt{\frac{H}{0.026}}.
$$
If waves produced by a storm have a height of 15 feet, what is the wind speed producing the waves?

Jaime Alvarez
Jaime Alvarez
Numerade Educator
01:10

Problem 107

Explain why $\sqrt{-81}$ is not a real number.

Garrett Bess
Garrett Bess
Numerade Educator
View

Problem 108

Will a radical expression with an odd index and a real number as the radicand always be a real number? Explain your answer.

Ed
Elita Dumaine
Numerade Educator
View

Problem 109

Will a radical expression with an even index and a real number as the radicand always be a real number? Explain your answer.

Ed
Elita Dumaine
Numerade Educator
00:12

Problem 110

a) To what is $\sqrt{a^{2}}$ equal?
b) To what is $\sqrt{a^{2}}$ equal if we know $a \geq 0$ ?

Tony Ni
Tony Ni
Numerade Educator
01:04

Problem 111

a) Evaluate $\sqrt{a^{2}}$ for $a=1.3$.
b) Evaluate $\sqrt{a^{2}}$ for $a=-1.3$.

Julie Silva
Julie Silva
Numerade Educator
00:43

Problem 112

a) Evaluate $\sqrt{-x}$ for $x=-81$.
b) Evaluate $-\sqrt{-x}$ for $x=-81$.
c) Evaluate $-\sqrt{x}$ for $x=-81$.

AG
Ankit Gupta
Numerade Educator
02:14

Problem 113

For what values of $x$ will $\sqrt{(x-1)^{2}}=x-1$ ? Explain how you determined your answer.

AG
Ankit Gupta
Numerade Educator
00:40

Problem 114

For what values of $x$ will $\sqrt{(x+3)^{2}}=x+3$ ? Explain how you determined your answer.

Vivek Kumar
Vivek Kumar
Numerade Educator
01:00

Problem 115

For what values of $x$ will $\sqrt{(2 x-6)^{2}}=2 x-6$ ? Explain how you determined your answer.

Jeffrey Morris
Jeffrey Morris
Numerade Educator
06:42

Problem 116

For what values of $x$ will $\sqrt{(3 x-8)^{2}}=3 x-8$ ? Explain how you determined your answer.

Vishal Parmar
Vishal Parmar
Numerade Educator
00:31

Problem 117

a) For what values of $a$ is $\sqrt{a^{2}}=|a|$ ?
b) For what values of $a$ is $\sqrt{a^{2}}=a$ ?
c) For what values of $a$ is $\sqrt[3]{a^{3}}=a$

AG
Ankit Gupta
Numerade Educator
00:40

Problem 118

Under what circumstances is the expression $\sqrt[n]{x}$ not a real number?

Victor Salazar
Victor Salazar
Numerade Educator
00:17

Problem 119

Explain why the expression $\sqrt[n]{x^{n}}$ is a real number for any real number $x$.

K B
K B
Numerade Educator
00:32

Problem 120

Under what circumstances is the expression $\sqrt[n]{x^{m}}$ not a real number?

Victor Salazar
Victor Salazar
Numerade Educator
00:29

Problem 121

Determine the domain of $\frac{\sqrt{x+5}}{\sqrt[3]{x+5}}$. Explain how you

Amy Jiang
Amy Jiang
Numerade Educator
02:28

Problem 122

Determine the domain of $\frac{\sqrt[3]{x-2}}{\sqrt[6]{x+1}}$. Explain how you determined your answer.

Taylor Shimono
Taylor Shimono
Numerade Educator
10:06

Problem 123

If $f(x)=-\sqrt{x}$, can $f(x)$ ever be
a) greater than 0 ,
b) equal to 0 ,
c) less than 0 ?
Explain your answers.

Leon Druch
Leon Druch
Numerade Educator
02:19

Problem 124

If $f(x)=\sqrt{x+5}$, can $f(x)$ ever be
a) less than 0 ,
b) equal to 0 ,
c) greater than 0 ?
Explain your answers.

Noah Musser
Noah Musser
Numerade Educator
00:29

Problem 125

In this activity, you will determine the conditions under which certain properties of radicals are true. We will discuss these properties later in this chapter. Discuss and answer these exercises as a group.
The property $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{a b}$, called the multiplication property for radicals, is true for certain real numbers $a$ and $b$. By substituting values for $a$ and $b$, determine under what conditions this property is true.

Nick Johnson
Nick Johnson
Numerade Educator
00:29

Problem 126

In this activity, you will determine the conditions under which certain properties of radicals are true. We will discuss these properties later in this chapter. Discuss and answer these exercises as a group.
The property $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$, called the division property for radicals, is true for certain real numbers $a$ and $b$. By substituting values for $a$ and $b$, determine under what conditions this property is true.

Nick Johnson
Nick Johnson
Numerade Educator
01:28

Problem 127

Factor.
$9 a x-3 b x+12 a y-4 b y$

Allison Knapp
Allison Knapp
Numerade Educator
00:21

Problem 128

Factor.
$3 x^{3}-18 x^{2}+24 x$

Ramzi Deek
Ramzi Deek
Numerade Educator
00:38

Problem 129

Factor.
$8 x^{4}+10 x^{2}-3$

Erika Bustos
Erika Bustos
Numerade Educator
00:36

Problem 130

Factor.
$x^{3}-\frac{8}{27} y^{3}$

Erika Bustos
Erika Bustos
Numerade Educator