Deck 8: Roots, Radicals, and Root Functions

Question 1

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{64}$

A) 4096
B) 8
C) $\frac{1}{64}$
D) Not a real number

Answer 1

8

Question 2

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{-100}$

A) $\frac{10}{100}$
B) 10
C) 10,000
D) Not a real number

Answer 2

Not a real number

Question 3

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{-324}$

A) 18
B) Not a real number
C) 104,976
D) $\frac{1}{324}$

Answer 3

Not a real number

Question 4

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{441}$

A) Not a real number
B) 194,481
C) $\frac{1}{441}$
D) 21

Question 5

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{\frac{81}{16}}$

A) $\frac{9}{4}$

B) $\frac{5}{2}$

C) 5

D) $\frac{9}{5}$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $-\sqrt{441}$

A) -21
B) Not a real number
C) -220
D) 21

Question 7

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt{0.0081}$

A) 0.009
B) 0.09
C) 0.9
D) 0.1

Question 8

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt[4]{1296}$

A) 6
B) 36
C) 7
D) 5

Question 9

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $-\sqrt[4]{625}$

A) -4
B) -25
C) -5
D) Not a real number

Question 10

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt[4]{-625}$

A) -5
B) Not a real number
C) 5
D) -25

Question 11

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt[4]{\frac{625}{81}}$

A) $\frac{625}{81}$

B) $\frac{5}{3}$

C) $\frac{125}{27}$

D) $\frac{25}{9}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt[5]{-243}$

A) 3
B) -3
C) 15
D) -15

Question 13

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $\sqrt[6]{64}$

A) $\frac{32}{3}$
B) 12
C) -2
D) 2

Question 14

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.

- $-\sqrt[5]{\frac{1}{1024}}$

A) $-\frac{1}{4}$

B) $-\frac{5}{1024}$

C) -4

D) $\varnothing$

Question 15

Graph the function and give its domain and its range.

- $f(x)=\sqrt{x-5}$

A) $[-5, \infty) ;[0, \infty)$


B) $[5, \infty) ;[0, \infty)$



C) $[0, \infty) ;[5, \infty)$
11eec209_bccb_efc3_8afd_c702d6ef0a5f_TB10232_00

D) $[0, \infty) ;[-5, \infty)$

Question 16

Graph the function and give its domain and its range.

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

A) $[-1, \infty)$ ; $[0, \infty)$



B) $[0, \infty)$ ; $[-1, \infty)$


C) $[1, \infty) ;[0, \infty)$


D) $[0, \infty) ;[1, \infty)$

Question 17

Graph the function and give its domain and its range.

- $f(x)=\sqrt[3]{x+3}$

A) $(-\infty, \infty) ;[3, \infty)$


B) $(-\infty, \infty) ;(-\infty, \infty)$


C) $(-\infty, \infty) ;[-3, \infty)$


D) $(-\infty, \infty) ;(3, \infty)$

Question 18

Graph the function and give its domain and its range.

- $f(x)=\sqrt[3]{x}-3$

A) $(-\infty, \infty) ;(-\infty, \infty)$


B) $(-\infty, \infty) ;(-3, \infty)$


C) $(-\infty, \infty) ;[3, \infty)$


D) $(0, \infty) ;(-\infty, \infty)$

Question 19

Simplify the root.

- $\sqrt[3]{\mathrm{x}^{3}}$

A) $x$
B) $|-x|$
C) $-x$
D) $|x|$

Question 20

Simplify the root.

- $-\sqrt{x^{12}}$

A) $-\left|x^{6}\right|$
B) $x^{6}$
C) $-x^6$
D) $\left|-x^{6}\right|$

Question 21

Simplify the root.

- $-\sqrt[3]{x^{21}}$

A) $\left|-x^{7}\right|$
B) $x^{7}$
C) $-x^{7}$
D) $-\left|x^{7}\right|$

Question 22

Simplify the root.

- $-\sqrt[4]{\mathrm{x}^{28}}$

A) $x^{7}$
B) $-\left|x^{7}\right|$
C) $-x^{7}$
D) $\left|-x^{7}\right|$

Question 23

Simplify the root.

- $\sqrt[5]{(-8)^{5}}$

A) Not a real number
B) 8
C) 64
D) -8

Question 24

Simplify the root.

- $\sqrt[6]{(-2)^{6}}$

A) -2
B) 4
C) Not a real number
D) 2

Question 25

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt{313}$

A) 17.697
B) 313.000
C) 17.689
D) 17.692

Question 26

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt{6050}$

A) 77.779
B) 6050.000
C) 77.787
D) 77.782

Question 27

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $-\sqrt{23}$

A) -4.796
B) -23.000
C) -4.801
D) -4.793

Question 28

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt{1.09}$

A) 1.044
B) 1.031
C) 1.000
D) 1.059

Question 29

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt[3]{67}$

A) 66.996
B) 4.066
C) 67.009
D) 4.062

Question 30

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt[4]{113}$

A) 3.282
B) 3.292
C) 3.274
D) 3.260

Question 31

Find the decimal approximation for the radical. Round the answer to three decimal places.

- $\sqrt[5]{-83}$

A) -2.420
B) -2.432
C) -2.441
D) -2.450

Question 32

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+1100$ , where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 729 parts are produced.

A) $\$ 6500$
B) $\$ 2900$
C) $\$ 22$
D) $\$ 2000$

Question 33

The cost of manufacturing clocks is given by $c=49 \sqrt{n+9}$ , where $c$ is the total cost and $n$ is the number produced. What is the cost when no clocks are produced?

A) 441
B) 49
C) 147
D) 21

Question 34

The radius of a right circular cone is given by the formula $r=\sqrt{\frac{3 V}{\pi h}}$ , where $V$ is the volume and $h$ is the height. If the volume is 1302 cubic inches and the height is 14 inches, what is the radius? Use 3.14 for $\pi$ , and round your answer to the nearest tenth of an inch.

A) 0.1 inches
B) 5.4 inches
C) 9.9 inches
D) 9.4 inches

Question 35

The radius of a sphere is given by the formula $r=\sqrt{\frac{S}{4 \pi}}$ , where $S$ is the surface area. If the surface area is 8709 square inches, what is the radius? Use 3.14 for $\pi$ , and round your answer to the nearest tenth of an inch.

A) 46.7 inches
B) 82.7 inches
C) 0 inches
D) 26.3 inches

Question 36

The principal square root of 9 is 3.

Question 37

The negative square root of 25 is 5.

Question 38

The principal fifth root of -243 is 3 .

Question 39

The negative sixth root of 64 is -2 .

Question 40

Suppose a rectangle has length $\sqrt{85}$ and width $\sqrt{99}$ . Which of the following is the best estimate of its area?

A) 172
B) 28
C) 38
D) 90

Question 41

Suppose a rectangle has length $\sqrt{40}$ and width $\sqrt{79}$ . Which of the following is the best estimate of its perimeter?

A) 54
B) 30
C) 21
D) 81

Question 42

If $a<0$ , which of the following correctly describes $-\sqrt{-a}$ ?

A) Zero
B) Positive
C) Negative
D) Not a real number

Question 43

Simplify the expression involving rational exponents.

- $1444^{1 / 2}$

A) 38
B) 152
C) 19
D) 76

Question 44

Simplify the expression involving rational exponents.

- $512^{1 / 3}$

A) 12,288
B) 8
C) 24
D) 4096

Question 45

Simplify the expression involving rational exponents.

- $256^{1 / 4}$

A) 4
B) 64
C) 1024
D) 16

Question 46

Simplify the expression involving rational exponents.

- $216^{4 / 3}$

A) 1296
B) 7776
C) 279,936
D) 46,656

Question 47

Simplify the expression involving rational exponents.

- $81^{5 / 4}$

A) 243
B) 2187
C) 6561
D) 19,683

Question 48

Simplify the expression involving rational exponents.

- $77764 / 5$

A) 1,679,616
B) 1296
C) 279,936
D) 10,077,696

Question 49

Simplify the expression involving rational exponents.

- $(-8)^{2 / 3}$

A) -2
B) -4
C) 4
D) Not a real number

Question 50

Simplify the expression involving rational exponents.

- $(-4)^{1 / 2}$

A) -1
B) -2
C) Not a real number
D) 2

Question 51

Simplify the expression involving rational exponents.

- $-\left(\frac{25}{49}\right)^{1 / 2}$

A) Not a real number

B) $-\frac{25}{98}$

C) $-\frac{5}{7}$

D) $\frac{7}{5}$

Question 52

Simplify the expression involving rational exponents.

- $\left(\frac{16}{49}\right)^{-1 / 2}$

A) $\frac{8}{49}$

B) $\frac{4}{7}$

C) Not a real number

D) $\frac{7}{4}$

Question 53

Simplify the expression involving rational exponents.

- $9^{-3 / 2}$

A) $\frac{1}{27}$

B) Not a real number

C) $-\frac{27}{2}$

D) -27

Question 54

Simplify the expression involving rational exponents.

- $\left(-\frac{64}{125}\right)^{-4 / 3}$

A) $\frac{256}{625}$

B) $-\frac{256}{625}$

C) $\frac{625}{256}$

D) Not a real number

Question 55

Simplify the expression involving rational exponents.

- $\left(\frac{64}{729}\right)^{-2 / 3}$

A) $\frac{81}{16}$

B) $\frac{729}{64}$

C) $\frac{16}{81}$

D) $\frac{64}{729}$

Question 56

Simplify the expression involving rational exponents.

- $216^{-1 / 3}$

A) -6

B) $\frac{1}{6}$

C) $\frac{1}{7}$

D) $-\frac{1}{6}$

Question 57

Write with radicals. Assume that all variables represent positive real numbers.

- $(\mathrm{mn})^{1 / 6}$

A) $\frac{1}{\sqrt[6]{m n}}$

B) $(\sqrt{m n})^{6}$

C) $\sqrt[6]{m n}$

D) $(\mathrm{mn})^{-6}$

Question 58

Write with radicals. Assume that all variables represent positive real numbers

- $\left(x^{8} y^{8}\right)^{1 / 3}$

A) $(\sqrt[3]{x y})^{8}$

B) $x^{24} y^{24}$

C) $\frac{1}{(\sqrt[3]{x y})^{8}}$

D) $(\sqrt[8]{x y})^{3}$

Question 59

Write with radicals. Assume that all variables represent positive real numbers

- $\left(5 p y^{2}\right)^{1 / 3}$

A) $\sqrt[5]{5 p y}$

B) $\sqrt{5 p y^{2}}$

C) $\sqrt[3]{5 p y}$

D) $\sqrt[3]{5 p y^{2}}$

Question 60

$\left(7 m^{4}+3 k^{2}\right)^{-4 / 3}$

A) $\frac{1}{\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}}$

B) $\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}$

C) $\frac{1}{\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}}$

D) $\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}$

Question 61

Write with radicals. Assume that all variables represent positive real numbers

- $(4 m+n)^{4 / 5}$

A) $\sqrt[4]{4 m+n^{5}}$

B) $\sqrt[5]{4 m+n^{4}}$

C) $\sqrt[5]{(4 m+n)^{4}}$

D) $\sqrt[4]{(4 m+n)^{5}}$

Question 62

Write with radicals. Assume that all variables represent positive real numbers

- $9^{1 / 2}$

A) $\sqrt{9}$
B) 4.5
C) $\sqrt{3}$
D) 3

Question 63

Write with radicals. Assume that all variables represent positive real numbers

- $(5 x)^{3 / 7}+(4 y)^{3 / 5}$

A) $\left(\sqrt[7]{5}^{3}+(\sqrt[5]{4})^{3}\right.$

B) $\left(\sqrt[7]{5}^{3} x+(\sqrt[5]{4})^{3} y\right.$

C) $(\sqrt[7]{5 x})^{3}+\left(\sqrt[5]{4 y}^{3}\right.$

D) $\left(\sqrt[3]{5 x}^{7}+\left(\sqrt[3]{4 y}^{5}\right.\right.$

Question 64

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt[3]{5^{12}}$

A) $\sqrt[3]{5^{12}}$

B) 625

C) 125

D) 3125

Question 65

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt{u^{32}}$

A) $\sqrt{\mathrm{u}^{16}}$
B) $\sqrt{\mathrm{u}^{32}}$
C) $u^{5.657}$
D) $\mathrm{u}^{16}$

Question 66

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt{z^{10}}$

A) $z^{5}$
B) $\frac{z}{2}$
C) $z^{20}$
D) $2 \mathrm{z}$

Question 67

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt[3]{x^{21}}$

A) $\frac{z}{3}$
B) $x^{63}$
C) $x^{7}$
D) $3 z$

Question 68

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt[7]{\mathrm{x}} \cdot \sqrt{\mathrm{x}}$

A) $\sqrt[7]{x^{2}}$
B) $\sqrt[14]{x^{9}}$
C) $\sqrt[9]{2 x}$
D) $\sqrt[9]{x^{2}}$

Question 69

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt[3]{\mathrm{r}} \cdot \sqrt[7]{\mathrm{r}^{3}}$

A) $\sqrt[21]{\mathrm{r}^{4}}$
B) $\sqrt[21]{\mathrm{r}^{16}}$
C) $\sqrt[10]{\mathrm{r}^{3}}$
D) $\sqrt[10]{r^{4}}$

Question 70

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\sqrt[4]{9 x^{6}}$

A) $\sqrt[x]{3 x^{2}}$
B) $3 x^{3}$
C) $\sqrt[4]{9 x^{6}}$
D) $\sqrt{3 x^{3}}$

Question 71

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$

A) $\sqrt[2]{x^{5}}$

B) $\sqrt[63]{x^{10}}$

C) $\sqrt[16]{x^{5}}$

D) $\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$

Question 72

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.

- $\frac{\sqrt[6]{\mathrm{r}^{5}}}{\sqrt[8]{\mathrm{r}^{3}}}$

A) $\sqrt[48]{r^{22}}$

B) $\frac{\sqrt[6]{r^{5}}}{\sqrt[8]{r^{3}}}$

C) $\mathrm{r}$

D) $\sqrt[24]{\mathrm{r}^{11}}$

Question 73

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $x^{1 / 7} \cdot x^{6 / 7}$

A) $\frac{1}{x}$

B) $x^{6 / 49}$

C) $x$

D) $x^{6 / 7}$

Question 74

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\frac{y^{9 / 8}}{y^{5 / 8}}$

A) $y^{1 / 2}$

B) $\frac{1}{y}$

C) $y$

D) $y^{9 / 8}$

Question 75

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\left(b^{4}\right)^{5 / 4}$

A) $b^{5 / 16}$

B) $b^{9 / 4}$

C) $b^{5}$

D) $\mathrm{b}^{1 / 4}$

Question 76

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $z^{-2 / 7} \cdot z^{3 / 7}$

A) $z^{1 / 7}$

B) $z^{6 / 7}$

C) $z^{-1 / 7}$

D) $z^{7 / 6}$

Question 77

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\left(\frac{x^{4}}{y^{-8}}\right)^{1 / 4}$

A) $x y$

B) $x y^{1 / 2}$

C) $\frac{x}{y^{2}}$

D) $x y^{2}$

Question 78

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\left(243 \mathrm{k}^{5} \mathrm{~m}^{-10}\right)^{1 / 5}$

A) $\frac{5 \mathrm{k}}{\mathrm{m}^{2}}$

B) $3 \mathrm{~km}^{2}$

C) $5 \mathrm{~km}^{2}$

D) $\frac{3 \mathrm{k}}{\mathrm{m}^{2}}$

Question 79

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\left(5 \mathrm{a}^{1 / 7} \mathrm{~b}^{5 / 7}\right)^{3}$

A) $125(a b)^{15 / 7}$

B) $5 a^{3 / 7} b^{15 / 7}$

C) $15 \mathrm{a}^{3 / 7} \mathrm{~b}^{5 / 7}$

D) $125 a^{3 / 7} b^{15 / 7}$

Question 80

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.

- $\left(16 \frac{a^{3} b^{-4}}{a^{-1} b^{4}}\right)^{1 / 4}$

A) $2 a b^{2}$

B) $\frac{4 a}{b^{2}}$

C) $\frac{2 \mathrm{a}}{\mathrm{b}^{2}}$

D) $\frac{4 b^{2}}{a}$