Algebra 2

Prentice Hall, Basia Kennedy, Dan Ramirez

Chapter 7

Radical Functions And Rational Exponents

Educators

KM
AG

Problem 1

Find all the real square roots of each number.
$$
225
$$

KM
Kimberly M.
Numerade Educator

Problem 2

Find all the real square roots of each number.
$$
0.0049
$$

Aditya B.
Numerade Educator

Problem 3

Find all the real square roots of each number.
$$
-\frac{1}{121}
$$

KM
Kimberly M.
Numerade Educator

Problem 4

Find all the real square roots of each number.
$$
\frac{64}{169}
$$

Aditya B.
Numerade Educator

Problem 5

Find all the real cube roots of each number.
$$
-64
$$

KM
Kimberly M.
Numerade Educator

Problem 6

Find all the real cube roots of each number.
$$
0.125
$$

Aditya B.
Numerade Educator

Problem 7

Find all the real cube roots of each number.
$$
-\frac{27}{216}
$$

KM
Kimberly M.
Numerade Educator

Problem 8

Find all the real cube roots of each number.
$$
0.000343
$$

Aditya B.
Numerade Educator

Problem 9

Find all the real fourth roots of each number.
$$
16
$$

KM
Kimberly M.
Numerade Educator

Problem 10

Find all the real fourth roots of each number.
$$
-16
$$

Aditya B.
Numerade Educator

Problem 11

Find all the real fourth roots of each number.
$$
0.0081
$$

KM
Kimberly M.
Numerade Educator

Problem 12

Find all the real fourth roots of each number.
$$
\frac{10,000}{81}
$$

Aditya B.
Numerade Educator

Problem 13

Find each real-number root.
$$
\sqrt{36}
$$

KM
Kimberly M.
Numerade Educator

Problem 14

Find each real-number root.
$$
-\sqrt{36}
$$

Aditya B.
Numerade Educator

Problem 15

Find each real-number root.
$$
\sqrt{-36}
$$

KM
Kimberly M.
Numerade Educator

Problem 16

Find each real-number root.
$$
\sqrt{0.36}
$$

Aditya B.
Numerade Educator

Problem 17

Find each real-number root.
$$
-\sqrt[3]{64}
$$

KM
Kimberly M.
Numerade Educator

Problem 18

Find each real-number root.
$$
\sqrt[3]{-64}
$$

Aditya B.
Numerade Educator

Problem 19

Find each real-number root.
$$
-\sqrt[4]{81}
$$

KM
Kimberly M.
Numerade Educator

Problem 20

Find each real-number root.
$$
\sqrt[4]{-81}
$$

Aditya B.
Numerade Educator

Problem 21

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{16 x^{2}}
$$

AG
Ankit G.
Numerade Educator

Problem 22

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{0.25 x^{6}}
$$

Aditya B.
Numerade Educator

Problem 23

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{x^{8} y^{18}}
$$

AG
Ankit G.
Numerade Educator

Problem 24

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{64 b^{48}}
$$

Aditya B.
Numerade Educator

Problem 25

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[3]{-64 a^{3}}
$$

AG
Ankit G.
Numerade Educator

Problem 26

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[3]{27 y^{6}}
$$

Aditya B.
Numerade Educator

Problem 27

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[4]{x^{8} y^{12}}
$$

AG
Ankit G.
Numerade Educator

Problem 28

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[5]{32 y^{10}}
$$

Aditya B.
Numerade Educator

Problem 29

Geometry The formula for the volume of a sphere is $V=\frac{4}{3} \pi r^{3} .$ Find the radius to the nearest hundredth of a sphere with each volume.
$$
10 \mathrm{in} .^{3}
$$

AG
Ankit G.
Numerade Educator

Problem 30

Geometry The formula for the volume of a sphere is $V=\frac{4}{3} \pi r^{3} .$ Find the radius to the nearest hundredth of a sphere with each volume.
$$
20 \mathrm{ft}^{3}
$$

Aditya B.
Numerade Educator

Problem 31

Geometry The formula for the volume of a sphere is $V=\frac{4}{3} \pi r^{3} .$ Find the radius to the nearest hundredth of a sphere with each volume.
$$
0.45 \mathrm{cm}^{3}
$$

AG
Ankit G.
Numerade Educator

Problem 32

Geometry The formula for the volume of a sphere is $V=\frac{4}{3} \pi r^{3} .$ Find the radius to the nearest hundredth of a sphere with each volume.
$$
0.002 \mathrm{mm}^{3}
$$

Aditya B.
Numerade Educator

Problem 33

Find the two real-number solutions of each equation.
$$
x^{2}=100
$$

KM
Kimberly M.
Numerade Educator

Problem 34

Find the two real-number solutions of each equation.
$$
x^{4}=1
$$

Aditya B.
Numerade Educator

Problem 35

Find the two real-number solutions of each equation.
$$
x^{2}=0.25
$$

KM
Kimberly M.
Numerade Educator

Problem 36

Find the two real-number solutions of each equation.
$$
x^{4}=\frac{16}{81}
$$

Aditya B.
Numerade Educator

Problem 37

Arrange the numbers $\sqrt[3]{-64},-\sqrt[3]{-64}, \sqrt{64},$ and $\sqrt[6]{64}$ in order from least to greatest.

AG
Ankit G.
Numerade Educator

Problem 38

Boat Building Boat builders share an old rule of thumb for sailboats. The maximum speed $K$ in knots is 1.35 times the square root of the length $L$ in feet of the boat's waterline.
a. A customer is planning to order a sailboat with a maximum speed of 8 knots. How long should the waterline be?
b. How much longer would the waterline have to be to achieve a maximum speed of 10 knots?

Aditya B.
Numerade Educator

Problem 39

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[3]{0.125}
$$

KM
Kimberly M.
Numerade Educator

Problem 40

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[3]{\frac{8}{216}}
$$

Aditya B.
Numerade Educator

Problem 41

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[4]{0.0016}
$$

KM
Kimberly M.
Numerade Educator

Problem 42

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[4]{\frac{1}{256}}
$$

Aditya B.
Numerade Educator

Problem 43

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[4]{16 c^{4}}
$$

AG
Ankit G.
Numerade Educator

Problem 44

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[3]{81 x^{3} y^{6}}
$$

Aditya B.
Numerade Educator

Problem 45

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{144 x^{3} y^{4} z^{5}}
$$

AG
Ankit G.
Numerade Educator

Problem 46

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[5]{y^{20}}
$$

Aditya B.
Numerade Educator

Problem 47

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[5]{-y^{20}}
$$

KM
Kimberly M.
Numerade Educator

Problem 48

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[5]{k^{15}}
$$

Aditya B.
Numerade Educator

Problem 49

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[5]{-k^{15}}
$$

KM
Kimberly M.
Numerade Educator

Problem 50

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{(x+3)^{2}}
$$

Aditya B.
Numerade Educator

Problem 51

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt{(x+1)^{4}}
$$

KM
Kimberly M.
Numerade Educator

Problem 52

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[2 n]{x^{2 n}}
$$

Aditya B.
Numerade Educator

Problem 53

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[2 n]{x^{4 n}}
$$

KM
Kimberly M.
Numerade Educator

Problem 54

Simplify each radical expression. Use absolute value symbols when needed.
$$
\sqrt[2 n]{x^{6 n}}
$$

Aditya B.
Numerade Educator

Problem 55

Open-Ended Find three radical expressions that simplify to $-2 x^{2}$

AG
Ankit G.
Numerade Educator

Problem 56

Critical Thinking For what positive integers $n$ is each of the statements true?.
a. If $x^{n}=b,$ then $x$ is an $n$ th root of $b$
b. If $x^{n}=b,$ then $x=\sqrt[n]{b}$

Aditya B.
Numerade Educator

Problem 57

Writing Is 10 a first root of 10$?$ Explain.

AG
Ankit G.
Numerade Educator

Problem 58

Tell whether each equation is true for all, some, or no values of the variable. Explain your answers.
$$
\sqrt{x^{4}}=x^{2}
$$

Aditya B.
Numerade Educator

Problem 59

Tell whether each equation is true for all, some, or no values of the variable. Explain your answers.
$$
\sqrt{x^{6}}=x^{3}
$$

AG
Ankit G.
Numerade Educator

Problem 60

Tell whether each equation is true for all, some, or no values of the variable. Explain your answers.
$$
\sqrt[3]{x^{8}}=x^{2}
$$

Aditya B.
Numerade Educator

Problem 61

Tell whether each equation is true for all, some, or no values of the variable. Explain your answers.
$$
\sqrt[3]{x^{3}}=|x|
$$

AG
Ankit G.
Numerade Educator

Problem 62

Simplify each radical expression. $n$ is an even number.
$$
\sqrt[n]{m^{n}}
$$

Aditya B.
Numerade Educator

Problem 63

Simplify each radical expression. $n$ is an even number.
$$
\sqrt[n]{m^{2 n}}
$$

KM
Kimberly M.
Numerade Educator

Problem 64

Simplify each radical expression. $n$ is an even number.
$$
\sqrt[n]{m^{3 n}}
$$

Aditya B.
Numerade Educator

Problem 65

Simplify each radical expression. $n$ is an even number.
$$
\sqrt[n]{m^{4 n}}
$$

KM
Kimberly M.
Numerade Educator

Problem 66

Simplify each radical expression. $n$ is an odd number.
$$
\sqrt[n]{m^{n}}
$$

Aditya B.
Numerade Educator

Problem 67

Simplify each radical expression. $n$ is an odd number.
$$
\sqrt[n]{m^{2 n}}
$$

AG
Ankit G.
Numerade Educator

Problem 68

Simplify each radical expression. $n$ is an odd number.
$$
\sqrt[n]{m^{3 n}}
$$

Aditya B.
Numerade Educator

Problem 69

Simplify each radical expression. $n$ is an odd number.
$$
\sqrt[n]{m^{4 n}}
$$

AG
Ankit G.
Numerade Educator

Problem 70

Which equation has more than one real-number solution?
$$\begin{array}{llll}{\text { A. } x^{2}=0} & {\text { B. } x^{2}=1} & {\text { C. } x^{2}=-1} & {\text { D. } x^{3}=-1}\end{array}$$

Aditya B.
Numerade Educator

Problem 71

Which number is greatest?
$$
\begin{array}{lllll}{\text { F. } \sqrt{0.5}} & {\text { G. } \sqrt[3]{0.5}} & {\text { H. } \sqrt[4]{0.5}} & {\text { J. } \sqrt[5]{0.5}}\end{array}
$$

AG
Ankit G.
Numerade Educator

Problem 72

Which statement is NOT true?
$$
\begin{array}{ll}{\text { A. }-3=-\sqrt{9}} & {\text { B. }-3=-\sqrt{-9}} \\ {\text { C. }-3=\sqrt[3]{-27}} & {\text { D. }-3=-\sqrt[4]{81}}\end{array}
$$

Aditya B.
Numerade Educator

Problem 73

Absolute value symbols are needed when you simplify some of these expressions. Which ones are they?
$$\text { I. }\sqrt[3]{-x^{3} y^{6}} \quad \text { II. } \sqrt{x^{2} y^{4}} \quad \text { III. } \sqrt[4]{x^{8} y^{12}} \quad \text { IV. } \sqrt{x^{4} y^{6}}$$
F. II and III only
H. II, III and IV only
G. II and IV only
J. II, III and IV

AG
Ankit G.
Numerade Educator

Problem 74

For what values of $x$ and $y$ does $\sqrt{x^{2} y^{4}}$ equal $\sqrt[3]{x^{3}} y^{6} ?$ Explain your answer.

Aditya B.
Numerade Educator

Problem 75

Expand each binomial.
$$
(x+y)^{5}
$$

AG
Ankit G.
Numerade Educator

Problem 76

Expand each binomial.
$$
(2-3 y)^{4}
$$

Aditya B.
Numerade Educator

Problem 77

Expand each binomial.
$$
(3 x-5)^{6}
$$

AG
Ankit G.
Numerade Educator

Problem 78

Expand each binomial.
$$
(2 a-b)^{7}
$$

Aditya B.
Numerade Educator

Problem 79

Write each function in factored form. Check by multiplying.
$$
y=4 x^{3}-49 x
$$

KM
Kimberly M.
Numerade Educator

Problem 80

Write each function in factored form. Check by multiplying.
$$
y=81 x^{2}+36 x+4
$$

Aditya B.
Numerade Educator

Problem 81

Write each function in factored form. Check by multiplying.
$$
y=4 x^{3}+8 x^{2}+4 x
$$

KM
Kimberly M.
Numerade Educator

Problem 82

Write each function in factored form. Check by multiplying.
$$
y=12 x^{3}+14 x^{2}+2 x
$$

Aditya B.
Numerade Educator

Problem 83

Rewrite each equation in vertex form.
$$
y=3 x^{2}-7
$$

KM
Kimberly M.
Numerade Educator

Problem 84

Rewrite each equation in vertex form.
$$
y=-2 x^{2}+x-10
$$

Aditya B.
Numerade Educator

Problem 85

Rewrite each equation in vertex form.
$$
y=\frac{x^{2}}{4}+2 x-1
$$

KM
Kimberly M.
Numerade Educator