Deck 7: Roots, Radicals, and Complex Numbers

Question 1

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 5 ] { \frac { 243 } { 32 } }$$

A) $\frac { 27 } { 8 }$
B) $\frac { 81 } { 16 }$
C) $\frac { 3 } { 2 }$
D)not a real number

Answer 1

$\frac { 3 } { 2 }$

Question 2

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 3 ] { - 343 }$$

A)-7
B)49
C)19
D)not a real number

Answer 2

-7

Question 3

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $- \sqrt { 64 }$

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

Answer 3

-8

Question 4

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 4 ] { 16 }$$

A)8
B)2
C)16
D)not a real number

Question 5

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 3 ] { \frac { 1 } { 27 } }$$

A)0.19
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 5 }$
D)not a real number

Question 6

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

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

A)243
B)3
C)-3
D)not a real number

Question 7

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 3 ] { 343 }$$

A)49
B)7
C)19
D)not a real number

Question 8

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

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

A)-3
B)-243
C)3
D)not a real number

Question 9

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt { 29 }$$

A)5
B)5.4
C)5.39
D)not a real number

Question 10

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $\sqrt { \frac { 36 } { 169 } }$

A) $\frac { 3 } { 7 }$
B) $\frac { 6 } { 13 }$
C) $\frac { 3 } { 14 }$
D)137

Question 11

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

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

A)-3
B)-36
C)-12
D)not a real number

Question 12

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $\sqrt { \frac { 1 } { 9 } }$

A) $\frac { 1 } { 81 }$
B) $\frac { 1 } { 3 }$
C)3
D)9

Question 13

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $\sqrt { - 16 }$

A)4
B)256
C)-4
D)not a real number

Question 14

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

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

A)0
B)0.67
C) $\frac { 4 } { 9 }$
D)0.22

Question 15

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$- \sqrt { 58.9 }$$

A)-7.66
B)-7.67
C)7.67
D)not a real number

Question 16

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 4 ] { \frac { 1 } { 625 } }$$

A) $\frac { 1 } { 100 }$
B) $\frac { 1 } { 20 }$
C) $\frac { 1 } { 5 }$
D)not a real number

Question 17

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

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

A)-36
B)-12
C)-3
D)not a real number

Question 18

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$- \sqrt [ 3 ] { - 343 }$$

A)7
B)-7
C)-18.52
D)not a real number

Question 19

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $\sqrt { 25 }$

A)625
B)5
C) $\frac { 1 } { 25 }$
D)not a real number

Question 20

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$- \sqrt [ 3 ] { 125 }$$

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

Question 21

Write as an absolute value.

- $$\sqrt { ( 11 x - 3 y ) ^ { 2 } }$$

A) $11 x + 3 y$
B) $11 x - 3 y$
C) $| 11 x - 3 y |$
D) $| 11 x + 3 y |$

Question 22

Use absolute value to evaluate.

- $$\sqrt { ( 4 ) ^ { 2 } }$$

A) $\frac { 1 } { 16 }$
B)256
C)4
D)not a real number

Question 23

Use absolute value to evaluate.

- $$\sqrt { ( 15.7 ) ^ { 2 } }$$

A)-15.7
B)15.7
C)246.49
D)not a real number

Question 24

Use absolute value to evaluate.

- $$\sqrt [ 4 ] { ( - 2 ) ^ { 4 } }$$

A)-2
B)16
C)2
D)not a real number

Question 25

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 4 ] { - \frac { 1 } { 81 } }$$

A) $\frac { 1 } { 3 }$
B)19
C) $- \frac { 1 } { 3 }$
D)not a real number

Question 26

Write as an absolute value.

- $\sqrt { z ^ { 2 } - 12 z + 36 }$

A)z + 6
B) $$\left| z ^ { 2 } - 12 z + 36 \right|$$
C) $| z - 6 |$
D)z - 6

Question 27

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.

- $\text { Find } g ( - 3 ) \text { if } g ( x ) = \sqrt { 25 - 5 x }$

A)6.325
B)5
C)4.472
D)not a real number

Question 28

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.

- $\text { Find } f ( - 3 ) \text { if } f ( x ) = \sqrt { x + 19 }$

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

Question 29

Use absolute value to evaluate.

- $$\sqrt { \left( - \frac { 49 } { 4 } \right) ^ { 2 } }$$

A) $\frac { 7 } { 2 }$
B) $\frac { 49 } { 4 }$
C) $- \frac { 7 } { 2 }$
D)not a real number

Question 30

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.

- $\text { Find } f ( 0 ) \text { if } f ( x ) = \sqrt { x ^ { 2 } + 7 x }$

A)7
B)2.646
C)7.483
D)0

Question 31

Write as an absolute value.

- $\sqrt { w ^ { 24 } }$

A) $\left| w ^ { 12 } \right|$
B) $w ^ { 12 }$
C) $w ^ { 22 }$
D) $-w^{ 12}$

Question 32

Write as an absolute value.

- $\sqrt { 49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } }$

A) $| 7 x + 3 y |$
B) $7 x - 3 y$
C) $| 7 x - 3 y |$
D) $7 x + 3 y$

Question 33

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.

- $\text { Find } r ( 18 ) \text { if } r ( x ) = \frac { x } { 3 } + \sqrt { 2 x } - 2$

A)14
B)-2
C)10
D)2

Question 34

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.

- $$\sqrt [ 4 ] { 104 }$$

A)3.2
B)26
C)3.19
D)not a real number

Question 35

Write as an absolute value.

- $$\sqrt { \left( 11 x ^ { 6 } - 7 y ^ { 4 } \right) ^ { 2 } }$$

A) $\left| 11 x ^ { 6 } - 7 y ^ { 4 } \right|$
B) $11 x ^ { 6 } - 7 y ^ { 4 }$
C) $11 x ^ { 3 } - 7 y ^ { 2 }$
D) $\left| 11 x ^ { 3 } - 7 y ^ { 2 } \right|$

Question 36

Write as an absolute value.

- $\sqrt { ( x + 2 ) ^ { 2 } }$

A)x + 2
B) $| x + 2 |$
C) $x ^ { 2 } + 4 x + 4$
D) $\left| x ^ { 2 } + 4 x + 4 \right|$

Question 37

Use absolute value to evaluate.

- $$\sqrt [ 5 ] { ( 2 ) ^ { 5 } }$$

A)32
B)2
C)-2
D)not a real number

Question 38

Use absolute value to evaluate.

- $\sqrt { ( - 2.43 ) ^ { 2 } }$

A)-2.43
B)5.9
C)2.43
D)not a real number

Question 39

Write as an absolute value.

- $$\sqrt { \mathrm { d } ^ { 2 } }$$

A) $| \mathrm { d } |$
B)d
C) $\mathrm { d } ^ { 2 }$
D)-d

Question 40

Use absolute value to evaluate.

- $\sqrt { ( - 2 ) ^ { 2 } }$

A)16
B) $\frac { 1 } { 4 }$
C)2
D)not a real number

Question 41

Write the expression in radical form. Assume that all variables represent positive real numbers.

- $\left( 6 x ^ { 2 } y ^ { 3 } \right) ^ { 5 / 3 }$

A) $\left( \sqrt [ 5 ] { \frac { 6 } { 5 } x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$
B) $\left( \sqrt [ 5 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$
C) $\left( \sqrt [ 3 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$
D) $\left( \sqrt [ 3 ] { 2 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$

Question 42

Simplify the radical expression. Write the answer in radical form when appropriate.

- $\sqrt [ 3 ] { x ^ { 15 } }$

A) $x ^ { 3 }$
B) $x ^ { 12 }$
C) $x ^ { 5 }$
D) $x ^ { - 5 }$

Question 43

Evaluate if possible. If the expression is not a real number, so state.

- $16 ^ { 5 / 4 }$

A)128
B)512
C)256
D)32

Question 44

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $\sqrt [ 9 ] { 2 x + 5 y }$

A) $( 2 x + 5 y ) ^ { 1 / 9 }$
B) $\left( \frac { 2 } { 3 } x + \frac { 5 } { 3 } y \right) ^ { 1 / 3 }$
C) $( 2 x + 5 y ) ^ { 1 / 3 }$
D) $( 2 x + 5 y ) ^ { 3 }$

Question 45

Evaluate if possible. If the expression is not a real number, so state.

- $8 ^ { 4 / 3 }$

A)16
B)32
C)64
D)128

Question 46

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $( \sqrt { x } ) ^ { 11 }$

A) $x ^ { 11 / 5 }$
B) $x ^ { 6 }$
C)x5/11
D) $x ^ { - 11 / 5 }$

Question 47

Simplify the radical expression. Write the answer in radical form when appropriate.

- $\sqrt [ 20 ] { x ^ { 4 } }$

A) $\sqrt [ 5 ] { \frac { 1 } { x } }$
B) $\sqrt [ 4 ] { x }$
C) $\sqrt [ 16 ] { x }$
D) $\sqrt [ 5 ] { x }$

Question 48

Write the expression in radical form. Assume that all variables represent positive real numbers.

- $x ^ { 1 / 5 }$

A) $\sqrt { 5 x }$
B) $- \sqrt [ 6 ] { x }$
C) $\sqrt [ 6 ] { x }$
D) $\sqrt [ 6 ] { \frac { 1 } { x } }$

Question 49

Simplify the radical expression. Write the answer in radical form when appropriate.

- $\left( \sqrt [ 6 ] { x ^ { 5 } y z ^ { 5 } } \right) ^ { 3 }$

A) $x ^ { 10 } y ^ { 2 } z ^ { 10 }$
B) $\sqrt { x ^ { 5 } y z ^ { 5 } }$
C) $\sqrt { x ^ { 15 } y ^ { 3 } z ^ { 15 } }$
D) $x ^ { 5 } y ^ { 2 } z ^ { 5 }$

Question 50

Evaluate if possible. If the expression is not a real number, so state.

- $- 32 ^ { 1 / 5 }$

A)32
B)-8
C)-2
D)16

Question 51

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $\sqrt [ 6 ] { x }$

A) $x ^ { - 1 / 3 }$
B) $x ^ { - 3 }$
C) $x ^ { 3 }$
D) $\mathrm { x } ^ { 1 / 3 }$

Question 52

Write the expression in radical form. Assume that all variables represent positive real numbers.

- $x ^ { 7 / 3 }$

A)7 x3
B) $\sqrt [ 5 ] { x ^ { 7 } }$
C) $\sqrt [ 4 ] { x ^ { 7 } }$
D) $\sqrt [ 4 ] { x }$

Question 53

Write the expression in radical form. Assume that all variables represent positive real numbers.

- $( 7 x + 2 ) ^ { 2 / 7 }$

A) $\sqrt [ 7 ] { 7 x ^ { 2 } + 4 }$
B) $( \sqrt [ 7 ] { ( 7 x + 2 ) } ) ^ { 2 }$
C) $\sqrt [ 7 ] { 49 x ^ { 2 } + 4 }$
D) $( \sqrt [ 2 ] { ( 7 x + 2 ) } ) ^ { 7 }$

Question 54

Evaluate if possible. If the expression is not a real number, so state.

- $16 ^ { 1 / 4 }$

A)16
B)8
C)2
D)32

Question 55

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $\sqrt [ 3 ] { x ^ { 13 } }$

A) $x ^ { 9 / 13 }$
B) $x ^ { - 13 / 9 }$
C) $x ^ { 13 / 9 }$
D) $x ^ { 4 }$

Question 56

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $\sqrt [ 9 ] { 4 x ^ { 12 } y ^ { 11 } }$

A) $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$
B) $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$
C) $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$
D) $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$

Question 57

Simplify the radical expression. Write the answer in radical form when appropriate.

- $\sqrt [ 4 ] { \sqrt [ 5 ] { x y } }$

A) $\sqrt [ 20 ] { x y }$
B) $\sqrt [ 5 ] { x y }$
C) $\sqrt [ 40 ] { x y }$
D) $\sqrt [ 4 ] { x y }$

Question 58

Evaluate if possible. If the expression is not a real number, so state.

- $16 ^ { 1 / 2 }$

A)16
B)4
C)8
D)2

Question 59

Simplify the radical expression. Write the answer in radical form when appropriate.

- $\left( \sqrt [ 4 ] { x ^ { 3 } y z ^ { 5 } } \right) ^ { 40 }$

A) $x ^ { 30 } y ^ { 10 } z ^ { 5 }$
B) $x ^ { 30 } y z ^ { 50 }$
C) $x ^ { 30 } y ^ { 10 } z ^ { 50 }$
D) $x ^ { 3 } y ^ { 10 } z ^ { 5 }$

Question 60

Write the expression in exponential form. Assume that all variables represent positive real numbers.

- $\sqrt [ 9 ] { 5 ^ { 11 } }$

A) $5 ^ { 11 / 2 }$
B) $5 ^ { 9 }$
C) $5 ^ { 2 / 11 }$
D) $5 ^ { - 11 / 2 }$

Question 61

Simplify. Write the answer in exponential form without negative exponents.

- $x ^ { - 1 / 5 } x ^ { - 5 / 3 }$

A) $\frac { 1 } { x ^ { 15 / 28 } }$
B) $\frac { 1 } { x ^ { 28 / 15 } }$
C) $x ^ { 1 / 3 }$
D) $\frac { 1 } { x ^ { 1 / 3 } }$

Question 62

Evaluate if possible. If the expression is not a real number, so state.

- $- 144 ^ { 1 / 2 }$

A)-12
B)48
C)24
D)- 72

Question 63

Simplify. Write the answer in exponential form without negative exponents.

- $\frac { x ^ { 3 } } { x ^ { - 1 / 5 } }$

A) $x ^ { 3 / 5 }$
B) $x ^ { 14 / 5 }$
C) $x ^ { 16 / 5 }$
D) $\frac { 1 } { x ^ { 3 / 5 } }$

Question 64

Evaluate if possible. If the expression is not a real number, so state.

- $27 ^ { - 1 / 3 }$

A)-3
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 27 }$
D) $- \frac { 1 } { 3 }$

Question 65

Evaluate if possible. If the expression is not a real number, so state.

- $( - 8 ) ^ { 4 / 3 }$

A)64
B)-16
C)16
D)not a real number

Question 66

Evaluate if possible. If the expression is not a real number, so state.

- $125 ^ { 1 / 3 } + 25 ^ { 1 / 2 }$

A)125
B) $54 \frac { 1 } { 6 }$
C)10
D)29

Question 67

Evaluate if possible. If the expression is not a real number, so state.

- $\left( 27 ^ { - 1 / 3 } \right) ^ { 0 }$

A) $\frac { 1 } { 3 }$
B)3
C)1
D)not a real number

Question 68

Evaluate if possible. If the expression is not a real number, so state.

- $\left( \frac { 16 } { 81 } \right) ^ { 1 / 4 }$

A)24
B) $\frac { 2 } { 3 }$
C) $\frac { 3 } { 2 }$
D)6

Question 69

Evaluate if possible. If the expression is not a real number, so state.

- $110 ^ { - 1 / 2 }$

A) $\frac { 1 } { 100 }$
B) $- \frac { 1 } { 10 }$
C) $\frac { 1 } { 10 }$
D)- 10

Question 70

Evaluate if possible. If the expression is not a real number, so state.

- $32^{4 / 5}$

A)16
B)256
C)512
D)128

Question 71

Simplify. Write the answer in exponential form without negative exponents.

- $\left( x ^ { - 1 / 2 } \right) ^ { - 1 / 6 }$

A) $x ^ { 12 }$
B) $\frac { 1 } { x ^ { 12 } }$
C) $x ^ { 1 / 12 }$
D) $\frac { 1 } { \mathrm { x } ^ { 1 / 12 } }$

Question 72

Evaluate if possible. If the expression is not a real number, so state.

- $$\left( \frac { 1 } { 243 } \right) ^ { - 1 / 5 }$$

A) $\frac { 1 } { 3 }$
B)3
C)-3
D) $\frac { - 1 } { 3 }$

Question 73

Evaluate if possible. If the expression is not a real number, so state.

- $( 16 ) ^ { - 5 / 4 }$

A)32
B) $- \frac { 1 } { 32 }$
C)-32
D) $\frac { 1 } { 32 }$

Question 74

Simplify. Write the answer in exponential form without negative exponents.

- $14 x ^ { 2 / 7 } \cdot 2 x ^ { - 9 / 4 }$

A) $\frac { 7 } { x ^ { 55 / 28 } }$
B) $\frac { 28 } { x ^ { 55 / 28 } }$
C) $- 28 x ^ { 55 / 28 }$
D) $\frac { 1 } { 28 x ^ { 55 / 28 } }$

Question 75

Simplify. Write the answer in exponential form without negative exponents.

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

A)x
B) $\frac { 1 } { x }$
C) $\mathrm { x } ^ { 1 / 9 }$
D) $\frac { 1 } { x ^ { 9 } }$

Question 76

Evaluate if possible. If the expression is not a real number, so state.

- $\left( \frac { 27 } { 64 } \right) ^ { - 1 / 3 }$

A) $- \frac { 4 } { 3 }$
B) $\frac { 3 } { 4 }$
C) $- \frac { 3 } { 4 }$
D) $\frac { 4 } { 3 }$

Question 77

Simplify. Write the answer in exponential form without negative exponents.

- $x ^ { - 9 / 2 }$

A) $- x ^ { 9 / 2 }$
B) $\frac { - 1 } { x ^ { 9 / 2 } }$
C) $\frac { 1 } { \mathrm { x } ^ { 2 / 9 } }$
D) $\frac { 1 } { x ^ { 9 / 2 } }$

Question 78

Evaluate if possible. If the expression is not a real number, so state.

- $( - 16 ) ^ { 1 / 2 }$

A)4
B)-4
C)256
D)not a real number

Question 79

Simplify. Write the answer in exponential form without negative exponents.

- $\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

A) $4 y ^ { 5 }$
B) $4 y ^ { 3 / 5 }$
C) $4 y ^ { 5 / 3 }$ DD) $y ^ { 5 / 3 }$

Question 80

Simplify. Write the answer in exponential form without negative exponents.

- $\left( x ^ { - 3 / 5 } \right) ^ { 1 / 7 }$

A) $- x ^ { 35 / 3 }$
B) $\frac { 1 } { x ^ { 3 / 35 } }$
C) $x ^ { 35 / 3 }$
D) $- \frac { 1 } { x ^ { 3 / 35 } }$