Deck 15: Roots and Radicals

Question 1

Find the root.

- $\sqrt [ 4 ] { 1 }$

A) $\frac { 1 } { 4 }$
B)1
C)4
D)Not a real number

Answer 1

1

Question 2

Approximate the square root to three decimal places.

- $\sqrt { 7 }$

A)7.000
B)2.651
C)2.646
D)2.643

Answer 2

2.646

Question 3

Find the root.

- $\sqrt [ 5 ] { 243 }$

A)4
B)3
C) $\frac { 243 } { 5 }$
D)Not a real number

Answer 3

3

Question 4

Approximate the square root to three decimal places.

- $\sqrt { 92 }$

A)9.597
B)9.589
C)9.592
D)92.000

Question 5

Find the cube root.

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

A)-7
B)7
C)-343
D)49

Question 6

Find the square root.

- $\sqrt { 324 }$

A)-18
B)18
C)162
D)Not a real number

Question 7

Find the root.

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

A)4.264
B)-3
C)9
D)Not real number

Question 8

Find the square root.

- $\sqrt { - 289 }$

A)17
B)-144
C)-17
D)Not a real number

Question 9

Find the root.

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

A)-3
B)3
C)9
D)Not real number

Question 10

Find the root.

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

A)3
B)-3
C) $- \frac { 243 } { 5 }$
D)Not a real number

Question 11

Find the cube root.

- $\sqrt [ 3 ] { 27 }$

A)3
B) $\pm 3$
C)5
D)9

Question 12

Find the square root.

- $- \sqrt { \frac { 1 } { 64 } }$

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

Question 13

Find the square root.

- $\sqrt { \frac { 1 } { 16 } }$

A) $\frac { 1 } { 4 }$
B) $\frac { 1 } { 256 }$
C)4
D)16

Question 14

Find the cube root.

- $\sqrt [ 3 ] { - 512 }$

A)-8
B)23
C)64
D)±8

Question 15

Find the square root.

-- $- \sqrt { 25 }$

A)5
B)-5
C)-12
D)Not a real number

Question 16

Find the square root.

- $\sqrt { 0.25 }$

A)5
B)0.005
C)0.05
D)0.5

Question 17

Find the root.

- $\sqrt [ 4 ] { 81 }$

A)4.264
B)9
C)3
D)Not real number

Question 18

Find the cube root.

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

A) $\frac { 1 } { 3 }$
B)3
C) $\frac { 1 } { \sqrt [ 3 ] { 3 } }$
D) $\frac { 1 } { 9 }$

Question 19

Find the root.

- $\sqrt [ 6 ] { 64 }$

A)8
B)2
C)4
D)Not a real number

Question 20

Find the square root.

- $\sqrt { \frac { 25 } { 441 } }$

A) $\frac { 2 } { 7 }$
B) $\frac { 5 } { 22 }$
C) $\frac { 3 } { 55 }$
D) $\frac { 5 } { 21 }$

Question 21

Find the root. Assume that all variables represent positive numbers.

- $\sqrt { \mathrm { x } ^ { 16 } \mathrm { y } 12 }$

A) $x ^ { 8 } y ^ { 12 }$
B) $x ^ { 14 } y ^ { 10 }$
C)x8y6
D)x16y6

Question 22

Find the root. Assume that all variables represent positive numbers.

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

A) $5 \sqrt { y }$
B) $y ^ { 10 }$
C) $y ^ { 5 }$
D) $y \sqrt { 10 }$

Question 23

Find the root. Assume that all variables represent positive numbers.

- $\sqrt [ 3 ] { 343 x ^ { 6 } }$

A) $49 x ^ { 2 }$
B) $18 x ^ { 2 }$
C) $7 x ^ { 2 }$
D)Not a real number

Question 24

Find the root. Assume that all variables represent positive numbers.

- $\sqrt [ 4 ] { \mathrm { y } ^ { 48 } }$

A) $y ^ { 44 }$
B) $y ^ { 12 }$
C) $y ^ { 24 }$
D) $\sqrt [ 4 ] { y ^ { 48 } }$

Question 25

Use the quotient rule and the product rule to simplify each radical.

- $\sqrt { \frac { 81 } { 25 } }$

A) $\frac { \sqrt { 9 } } { \sqrt { 5 } }$
B) $\frac { \sqrt { 9 } } { 5 }$
C)1
D) $\frac { 9 } { 5 }$

Question 26

Use the product rule to simplify the radical.

- $\sqrt { 15 }$

A)5
B) $5 \sqrt { 3 }$
C) $\sqrt { 15 }$
D) $3 \sqrt { 5 }$

Question 27

Use the product rule to simplify the radical.

- $- 8 \sqrt { 20 }$

A) $16 \sqrt { 5 }$
B) $5 \sqrt { 16 }$
C) $- 16 \sqrt { 5 }$
D) $- 5 \sqrt { 16 }$

Question 28

Find the root. Assume that all variables represent positive numbers.

- $\sqrt [ 3 ] { - 216 x ^ { 6 } }$

A) $36 x ^ { 2 }$
B) $- 6 x ^ { 2 }$
C) $14 x ^ { 2 }$
D)Not a real number

Question 29

Find the root. Assume that all variables represent positive numbers.

- $\sqrt { 64 x ^ { 10 } }$

A) $8 x ^ { 10 }$
B) $x ^ { 5 } \sqrt { 8 }$
C) $64 x ^ { 5 }$
D) $8 x ^ { 5 }$

Question 30

Use the quotient rule and the product rule to simplify each radical.

- $\sqrt { \frac { 13 } { 25 } }$

A) $\frac { 13 } { 5 }$
B) $\frac { \sqrt { 13 } } { 5 }$
C) $\frac { \sqrt { 13 } } { 25 }$
D) $\sqrt { \frac { 13 } { 25 } }$

Question 31

Use the product rule to simplify the radical.

- $6 \sqrt { 49 }$

A)42
B)13
C)21
D)147

Question 32

Find the root. Assume that all variables represent positive numbers.

- $\sqrt [ 3 ] { - 8 x ^ { 18 } y ^ { 30 } }$

A) $- 2 x ^ { 6 } y ^ { 10 }$
B) $4 x ^ { 6 } y ^ { 10 }$
C) $2 x ^ { 6 } y ^ { 10 }$
D) $- 2 x ^ { 9 } y ^ { 15 }$

Question 33

Find the root. Assume that all variables represent positive numbers.

- $- \sqrt [ 3 ] { - 125 x ^ { 18 } y ^ { 36 } }$

A) $5 x ^ { 6 } y ^ { 18 }$
B) $5 x ^ { 6 } y ^ { 12 }$
C) $- 5 x ^ { 18 } y ^ { 12 }$
D) $25 x ^ { 6 } y ^ { 12 }$

Question 34

Find the root. Assume that all variables represent positive numbers.

- $\sqrt { 144 m ^ { 20 } n ^ { 14 } }$

A) $12 m ^ { 10 } 0 ^ { 7 }$
B) $72 m ^ { 18 } n ^ { 12 }$
C) $72 m ^ { 10 } n ^ { 7 }$
D) $12 m ^ { 18 } n ^ { 12 }$

Question 35

Use the product rule to simplify the radical.

- $\sqrt { 54 }$

A)18
B)7
C) $6 \sqrt { 3 }$
D) $3 \sqrt { 6 }$

Question 36

Use the product rule to simplify the radical.

- $\sqrt { 117 }$

A) $\sqrt { 117 }$
B)39
C) $3 \sqrt { 13 }$
D) $9 \sqrt { 13 }$

Question 37

Approximate the square root to three decimal places.

- $\sqrt { 336 }$

A)18.335
B)18.330
C)18.327
D)336.000

Question 38

Use the product rule to simplify the radical.

- $\sqrt { 495 }$

A) $3 \sqrt { 55 }$
B) $15 \sqrt { 11 }$
C) $9 \sqrt { 55 }$
D) $33 \sqrt { 5 }$

Question 39

Find the root. Assume that all variables represent positive numbers.

- $\sqrt [ 3 ] { \mathrm { x } ^ { 24 } }$

A) $x ^ { 21 }$
B) $x ^ { 12 }$
C) $\sqrt [ 3 ] { x ^ { 24 } }$
D) $x ^ { 8 }$

Question 40

Use the quotient rule and the product rule to simplify each radical.

- $\sqrt { \frac { 1445 } { 9 } }$

A) $\sqrt { \frac { 1445 } { 9 } }$
B) $\frac { 17 \sqrt { 5 } } { 3 }$
C) $\frac { 289 \sqrt { 5 } } { 9 }$
D) $\frac { \sqrt { 1445 } } { 3 }$

Question 41

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \mathrm { y } ^ { 11 } }$ 11

A) $\sqrt { \mathrm { y } ^ { 11 } }$
B) $y \sqrt { y ^ { 9 } }$
C) $y ^ { 10 } \sqrt { y }$
D) $y ^ { 5 } \sqrt { y }$

Question 42

Use the quotient rule and the product rule to simplify each radical.

- $\sqrt { \frac { 300 } { 8100 } }$

A) $\sqrt { \frac { 3 } { 81 } }$
B) $\frac { \sqrt { 3 } } { 9 }$
C) $\sqrt { \frac { 300 } { 8100 } }$
D) $\frac { 10 \sqrt { 3 } } { 90 }$

Question 43

Use the quotient rule and the product rule to simplify each radical.

- $- \sqrt { \frac { 68 } { 121 } }$

A) $- \frac { \sqrt { 68 } } { 11 }$
B) $- \frac { 2 \sqrt { 17 } } { 11 }$
C) $- \sqrt { \frac { 68 } { 121 } }$
D) $- \frac { 34 } { 11 }$

Question 44

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \frac { 125 x ^ { 2 } y } { 49 } }$

A) $\frac { 5 x \sqrt { 5 y } } { 7 }$
B) $25 x \sqrt { 5 y }$
C) $x \sqrt { \frac { 125 y } { 7 } }$
D) $\frac { 5 \sqrt { 5 x ^ { 2 } y } } { 7 }$

Question 45

Simplify the radical.

- $\sqrt [ 3 ] { 256 }$

A) $3 \sqrt [ 8 ] { 256 }$
B) $4 \sqrt [ 3 ] { 4 }$
C)2
D)128

Question 46

Simplify the radical.

- $\sqrt [ 3 ] { \frac { 6 } { 125 } }$

A) $\frac { 6 } { 5 }$
B) $\frac { \sqrt [ 3 ] { 6 } } { 5 \sqrt { 5 } }$
C) $\sqrt [ 3 ] { \frac { 6 } { 125 } }$
D) $\frac { \sqrt [ 3 ] { 6 } } { 5 }$

Question 47

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { 343 y ^ { 2 } }$

A) $7 y ^ { 2 } \sqrt { 7 }$
B) $7 \sqrt { 7 }$
C) $7 y \sqrt { 7 }$
D) $7 \sqrt { 7 y ^ { 2 } }$

Question 48

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \frac { 150 a ^ { 2 } b } { c ^ { 2 } } }$

A) $\frac { 25 a \sqrt { 6 b } } { c }$
B) $\frac { a \sqrt { 150 b } } { c }$
C) $\frac { 5 \sqrt { 6 a ^ { 2 } b } } { c }$
D) $\frac { 5 a \sqrt { 6 b } } { c }$

Question 49

Add or subtract as indicated.

- $- 17 \sqrt { 10 } - 11 \sqrt { 10 }$

A) $- 6 \sqrt { 10 }$
B) $7 \sqrt { 10 }$
C) $- 28 \sqrt { 10 }$
D) $27 \sqrt { 10 }$

Question 50

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { 147 x ^ { 2 } }$

A) $3 x ^ { 2 } \sqrt { 7 }$
B)147x
C) $7 \sqrt { 3 x }$
D) $7 x \sqrt { 3 }$

Question 51

Simplify the radical.

- $\sqrt [ 3 ] { \frac { 54 } { 64 } }$

A) $\frac { \sqrt [ 3 ] { 54 } } { 4 }$
B) $\frac { 3 \sqrt { 6 } } { 4 \sqrt { 4 } }$
C) $\sqrt [ 3 ] { \frac { 54 } { 64 } }$
D) $\frac { 3 \sqrt [ 3 ] { 2 } } { 4 }$

Question 52

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \frac { 490 } { x ^ { 2 } } }$

A) $\frac { 7 \sqrt { 10 } } { x }$
B) $\frac { 70 } { x }$
C) $\frac { \sqrt { 490 } } { x }$
D) $\sqrt { \frac { 490 } { x ^ { 2 } } }$

Question 53

Simplify the radical.

- $\sqrt [ 3 ] { 16 }$

A) $3 \sqrt [ 4 ] { 2 }$
B) $2 \sqrt [ 3 ] { 2 }$
C)8
D)1

Question 54

Add or subtract as indicated.

- $25 \sqrt { 5 } - 5 \sqrt { 5 }$

A)20
B) $20 \sqrt { 5 }$
C) $30 \sqrt { 5 }$
D)100

Question 55

Add or subtract as indicated.

- $9 \sqrt { 6 } - 2 \sqrt { 6 }$

A) $11 \sqrt { 6 }$
B) $7 \sqrt { 12 }$
C) $7 \sqrt { 6 }$
D) $- 18 \sqrt { 12 }$

Question 56

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { 27 x ^ { 2 } y }$

A) $3 x ^ { 2 } \sqrt { 3 y }$
B) $3 x y \sqrt { 3 }$
C) $3 x y ^ { 2 } \sqrt { 3 }$
D) $3 x \sqrt { 3 y }$

Question 57

Simplify the radical.

- $\sqrt [ 3 ] { 648 }$

A)6
B)18
C) $6 \sqrt [ 3 ] { 18 }$
D) $6 \sqrt [ 3 ] { 3 }$

Question 58

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \frac { 29 } { x ^ { 4 } } }$

A) $\frac { \sqrt { 29 } } { x }$
B) $\frac { \sqrt { 29 x ^ { 4 } } } { x ^ { 4 } }$
C) $\frac { \sqrt { 29 } } { \sqrt { x ^ { 4 } } }$
D) $\frac { \sqrt { 29 } } { x ^ { 2 } }$

Question 59

Simplify the radical. Assume that all variables represent positive numbers.

- $\sqrt { \frac { x ^ { 17 } } { 36 } }$

A) $\frac { x ^ { 8 } x } { 6 }$
B) $\frac { x ^ { 8 } \sqrt { x } } { 6 }$
C) $\frac { \sqrt { x _ { 17 } } } { 6 }$
D) $\frac { x \sqrt { x ^ { 15 } } } { 6 }$

Question 60

Add or subtract as indicated.

- $\sqrt { 6 } + \sqrt { 6 }$

A) $\sqrt { 12 }$
B)6
C) $2 \sqrt { 6 }$
D)36

Question 61

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $6 \sqrt { 5 }$ + $2 \sqrt { 20 }$

A)- $2\sqrt { 5 }$
B) $10 \sqrt { 5 }$
C)- $10 \sqrt { 5 }$
D) $8\sqrt { 5 }$

Question 62

Add or subtract as indicated.

- $6 \sqrt { 10 } - 11 \sqrt { 10 } +2 \sqrt { 1 0 }$

A) $- 3 \sqrt { 10 }$
B) $- 7 \sqrt { 10 }$
C) $7 \sqrt { 10 }$
D) $3 \sqrt { 10 }$

Question 63

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $2 \sqrt { 45 }$ - $4 \sqrt {180 }$

A)- $18\sqrt { 5 }$
B)- $30 \sqrt { 5}$
C) $18 \sqrt { 5 }$
D) $30 \sqrt { 5 }$

Question 64

Add or subtract as indicated.

- $12 \sqrt { 13 } - 8 \sqrt { 13 } - \sqrt { 13 }$

A) $- 5 \sqrt { 13 }$
B) $3 \sqrt { 13 }$
C) $5 \sqrt { 13 }$
D) $4 \sqrt { 13 }$

Question 65

Add or subtract as indicated.

- $21 \sqrt { 7 } - 6 \sqrt { 7 }$

A) $27 \sqrt { 7 }$
B)105
C) $15 \sqrt { 7 }$
D)15

Question 66

Add or subtract as indicated.

- $3 \sqrt { 10 }$ +9- $9 \sqrt { 10 }$

A) $3 \sqrt {10 }$
B)9 + $6\sqrt { 10 }$
C)9 + $12 \sqrt { 10 }$
D)9 - $9 \sqrt { 10 }$

Question 67

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt {3a }$ - 5 $\sqrt {48a }$ - 5 $\sqrt {75a }$

A)-44 $\sqrt {3a }$
B)-44 $\sqrt {126a }$
C)-10 $\sqrt {3a }$
D)-10 $\sqrt {126a }$

Question 68

Add or subtract as indicated.

- $5 \sqrt { 7 } + \sqrt { 15 } -4\sqrt { 7}$

A) $\sqrt { 22 }$
B) $\sqrt { 7 }$ + $\sqrt { 15 }$
C) $\sqrt { 15 }$
D) $9\sqrt { 7 }$ + $\sqrt { 15 }$

Question 69

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { \frac { 2 } { 36 } } + \sqrt { \frac { 72 } { 25 } }$

A) $\frac { 2 } { 5 }$
B) $\frac { 41 \sqrt { 2 } } { 30 }$
C) $\frac { 41 \sqrt { 2 } } { 6 }$
D) $\frac { - 31 \sqrt { 2 } } { 30 }$

Question 70

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { 28 }$ + $\sqrt { 448 }$

A)70
B)-6 $\sqrt { 6 }$
C)10 $\sqrt { 14 }$
D)10 $\sqrt { 7 }$

Question 71

Add or subtract as indicated.

- $9 \sqrt { 6 } + 2 \sqrt { 6 } +9 \sqrt { 6 }$ +20

A) $20 \sqrt { 6 }$ +20
B)46
C) $20 \sqrt { 26 }$
D) $40 \sqrt { 6 }$

Question 72

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $x \sqrt { 6 x } + 5 \sqrt { 216 x ^ { 3 } } - 3 x \sqrt { 216 x }$

A) $2 x \sqrt { 6 x }$
B) $13 x \sqrt { 235 x }$
C) $13 x \sqrt { 6 x }$
D) $2 x \sqrt { 216 x }$

Question 73

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { 605 } + \sqrt { 32 } + \sqrt { 500 } + 6 \sqrt { 18 }$

A) $21 \sqrt { 5 } + 22 \sqrt { 2 }$
B) $21 \sqrt { 5 } + 7 \sqrt { 2 }$
C) $43 \sqrt { 7 }$
D) $221 \sqrt { 5 } + 70 \sqrt { 2 }$

Question 74

Simplify the expression. Assume all variables represent positive real numbers.

- $20 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$

A) $20 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$
B) $15 \sqrt [ 3 ] { 2 }$
C) $5 \sqrt [ 3 ] { 2 }$
D) $- 5 \sqrt [ 3 ] { 2 }$

Question 75

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { 144 } + \sqrt { 98 } + \sqrt { 25 } + \sqrt { 32 }$

A) $\sqrt { 98 } + \sqrt { 32 } + 17$
B) $11 \sqrt { 2 } + \sqrt { 144 } + \sqrt { 25 }$
C) $65 \sqrt { 2 } + 17$
D) $11 \sqrt { 2 } + 17$

Question 76

Add or subtract as indicated.

- $\sqrt { 13 } - 4 \sqrt { 13 }$

A) $- 3 \sqrt { 13 }$
B) $4 \sqrt { 13 }$
C) $- 3 \sqrt { 26 }$
D) $3 \sqrt { 13 }$

Question 77

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { 147 }$ + $4 \sqrt {75 }$ -10 $\sqrt { 108 }$

A)33 $\sqrt {3 }$
B)-75 $\sqrt {3 }$
C)-33 $\sqrt {3 }$
D)71 $\sqrt {3 }$

Question 78

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt { 6 x ^ { 2 } } + 3 \sqrt { 54 x ^ { 2 } } + 5 \sqrt { 54 x ^ { 2 } }$

A) $25 x \sqrt { 85 }$
B) $25 x \sqrt { 6 }$
C) $8 \times \sqrt { 85 }$
D) $8 x \sqrt { 6 }$

Question 79

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

- $\sqrt {3 }$ - 2 $\sqrt {108}$ - $4 \sqrt {48 }$

A)-6 $\sqrt {3 }$
B)-27 $\sqrt {3 }$
C)-6 $\sqrt {159 }$ .
D)-27 $\sqrt {159 }$

Question 80

Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers.

-- $6\sqrt { 72 }$ + $4 \sqrt {98 }$ +9 $\sqrt { 128 }$

A)64 $\sqrt { 2 }$
B)-6 $\sqrt {2 }$
C)-340 $\sqrt {2 }$
D)340 $\sqrt { 2 }$