Deck 7: Radicals and Complex Numbers

Question 1

Evaluate the radical expression $- ( \sqrt { 40 } ) ^ { 2 }$ without using a calculator. If not possible, state the reason.

A) -40
B) 1600
C) -1600
D) 40
E)not a real number

Answer 1

-40

Question 2

Classify the number $\sqrt { 23 }$ as rational or irrational.

A)rational
B)irrational

Answer 2

irrational

Question 3

Evaluate without using a calculator. $\left( - 2 ^ { 3 } \right) ^ { \frac { 5 } { 3 } }$

A)-32
B)-8
C)8
D)5
E)32

Answer 3

-32

Question 4

Simplify the expression $\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

A) $\frac{1}{5}$
B) $\frac { 1 } { 26 }$
C) 5
D) 10
E) 26

Question 5

Rewrite the expression $u ^ { 3 } \sqrt [ 3 ] { u }$ using rational exponents.

A) $u ^ { 2 / 3 }$
B) $u ^ { 8 / 3 }$
C) $u ^ { 10 / 3 }$
D) $u ^ { 7 / 3 }$
E) $u ^ { 4 / 3 }$

Question 6

Evaluate $64 ^ { - 4 / 3 }$ without using a calculator.

A) $\frac { 1 } { 512 }$
B)64
C) $\frac { 1 } { 64 }$
D) $\frac { 1 } { 256 }$
E)256

Question 7

Rewrite the expression $z ^ { 3 } \sqrt { y ^ { 3 } z ^ { 6 } }$ using rational exponents.

A) $y ^ { 3 } z ^ { 6 }$
B) $y ^ { 3 } z ^ { 3 }$
C) $y ^ { 3 / 2 } z ^ { 4 }$
D) $y ^ { 3 / 2 } z ^ { 6 }$
E) $y ^ { 3 / 2 } z ^ { 3 }$

Question 8

Evaluate the radical expression $\sqrt { - 12 }$ without using a calculator. If not possible, state the reason.

A) -12
B) -144
C) 144
D) 12
E)not a real number

Question 9

Evaluate the radical expression (if possible)without using a calculator. $\sqrt { ( - 10 ) ^ { 2 } }$

A) 100
B) -100
C) 10
D) -10
E)not possible

Question 10

State whether the number is a perfect square, a perfect cube, or neither.

A)perfect square
B)neither
C)perfect cube

Question 11

Find all of the cube roots of the perfect cube $\frac { 216 } { 125 }$ .

A) $\frac { 31 } { 18 }$
B) $\frac { 215 } { 124 }$
C) $\frac { 6 } { 5 }$
D) $\frac{5}{6}$
E) $\frac { 36 } { 25 }$

Question 12

Find all of the square roots of the perfect square $\frac{4}{9}$ .

A) $\frac{2}{3}$
B) $\pm \frac { 8 } { 27 }$
C) $\frac { 1 } { 2 }$
D) $\pm \frac { 2 } { 3 }$
E) $\pm \frac { 3 } { 4 }$

Question 13

Find the principal square root of $- \sqrt { 196 }$ , if possible. Do not use a calculator.

A)14
B) -14
C) -196
D) 196
E)no real roots

Question 14

Find the principal square root of $\sqrt { - 25 }$ , if possible. Do not use a calculator.

A)5
B) 25,-25
C) -5
D) $\sqrt { 5 } , - \sqrt { 5 }$
E)no real roots

Question 15

Classify the number $\sqrt { \frac { 1 } { 9 } }$ as rational or irrational.

A)rational
B)irrational

Question 16

Rewrite the expression using rational exponents. $\sqrt [ 4 ] { y ^ { 3 } } \sqrt [ 3 ] { y }$

A) $y ^ { \frac { 1 } { 6 } }$
B) $y ^ { \frac { 13 } { 12 } }$
C) $y ^ { \frac { 1 } { 4 } }$
D) $y ^ { \frac { 1 } { 3 } }$
E) $y ^ { \frac { 3 } { 4 } }$

Question 17

Rewrite the expression using rational exponents. $\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

A) $\frac { 1 } { x ^ { 2 / 3 } }$
B) $x ^ { 3 }$
C) $\frac { 1 } { x ^ { 2 } }$
D) $\frac { 1 } { x ^ { 3 } }$
E) $x ^ { 2 }$

Question 18

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 4 ] { 2 ^ { 4 } }$

A) 2
B) -16
C) 16
D) -2
E)not possible

Question 19

Simplify the expression $\frac { 13 y ^ { 4 / 3 } z ^ { - 1 / 5 } } { 28 y ^ { - 2 / 3 } z }$ .

A) $\frac { 14 y ^ { 2 } } { 29 z ^ { 6 / 5 } }$
B) $\frac { 13 y ^ { 2 } } { 28 z ^ { 6 / 5 } }$
C) $\frac { 13 y ^ { 2 } } { 28 z ^ { 4 / 5 } }$
D) $\frac { 13 y ^ { 2 } } { 28 z ^ { 1 / 5 } }$
E) $\frac { y ^ { 2 } } { 2 z ^ { 6 / 5 } }$

Question 20

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 3 ] { ( - 9 ) ^ { 3 } }$

A) 729
B) -729
C) -9
D) 9
E)not possible

Question 21

A stream of water moving at the rate of $v$ feet per second can carry particles of size $0.39 \sqrt { v }$ inches. Find the particle size (in inches)that can be carried by a stream flowing at the rate of $\frac { 3 } { 4 }$ foot per second. Round your answer to two decimal places.

A)0.29 $\text { inch }$
B)0.34 $\text { inch }$
C)0.62 $\text { inch }$
D)0.87 $\text { inch }$
E)0.47 $\text { inch }$

Question 22

Simplify the radical. $\sqrt { \frac { 77 } { 16 } }$

A) $\frac { \sqrt { 11 } } { 4 }$
B) $\frac { 11 \sqrt { 7 } } { 4 }$
C) $\frac { \sqrt { 7 } } { 4 }$
D) $\frac { \sqrt { 77 } } { 4 }$
E) $\frac { 7 \sqrt { 11 } } { 4 }$

Question 23

Evaluate $f ( 51 )$ , if possible. Round the answer to the nearest whole number. $f ( x ) = \sqrt [ 3 ] { 7 x - 14 }$

A)3
B)7
C)6
D)8
E)not a real number

Question 24

Simplify the radical $\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

A) $x ^ { 2 }$
B) $\frac { x ^ { 2 } } { 3 }$
C) $\frac { x } { 3 }$

D) $\frac { 1 } { 3 }$
E) $x ^ { 2 } \sqrt { 5 }$

Question 25

Simplify the radical expression. $\sqrt [ 4 ] { 64 u ^ { 4 } v ^ { 7 } }$

A) $8 | u | v \sqrt [ 4 ] { v ^ { 4 } }$
B) $4 | u | v ^ { 3 } \sqrt [ 4 ] { 2 }$
C) $8 | u | v ^ { 6 } \sqrt [ 4 ] { v }$
D) $4 | u | v ^ { 2 } \sqrt [ 4 ] { 2 v }$
E) $2 | u | v \sqrt [ 4 ] { 4 v ^ { 3 } }$

Question 26

Describe the domain of the function. $g ( x ) = \sqrt { 7 - 8 x }$

A) $x \geq \frac { 7 } { 8 }$
B) $x \leq \frac { 7 } { 8 }$
C) $x \geq \frac { 8 } { 7 }$
D) $x \leq \frac { 8 } { 7 }$
E)all real numbers

Question 27

Simplify the radical expression. $\sqrt { 192 x ^ { 14 } y ^ { 13 } }$

A) $8 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { 3 x }$
B) $24 x ^ { 6 } \left| y ^ { 7 } \right| \sqrt { x }$
C) $8 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { 3 y }$
D) $24 \left| x ^ { 7 } \right| y ^ { 6 } \sqrt { y }$
E) $8 \left| x ^ { 8 } \right| y ^ { 7 } \sqrt { 3 y }$

Question 28

Simplify the radical. $\sqrt { 0.0343 }$

A) $0.49 \sqrt { 7 }$
B) $0.7 \sqrt { 0.7 }$
C) $0.07 \sqrt { 7 }$
D) $0.07 \sqrt { 0.1 }$
E) $0.49 \sqrt { 0.1 }$

Question 29

Simplify the radical $\sqrt { 27 }$ , if possible.

A) $9 \sqrt { 3 }$
B) 27
C) $\sqrt { 3 }$
D) $3 \sqrt { 3 }$
E)cannot be simplified

Question 30

Simplify the radical $\sqrt { 242 }$ , if possible.

A) $11 \sqrt { 2 }$
B)2
C) $242 \sqrt { 2 }$
D)121
E)cannot be simplified

Question 31

Use a calculator to approximate $\frac { - 14 - 3 \sqrt { 2 } } { 2 }$ . Round your answer to three decimal places.

A)-9.121
B)-18.243
C)-11.243
D)-2.121
E)-7

Question 32

Use a calculator to approximate the value $\sqrt { 332 }$ , if possible. Round the answer to three decimal places.

A)18.554
B)18.000
C)18.221
D) -18.221
E)not a real number

Question 33

Simplify the radical $\sqrt { \frac { x ^ { 18 } } { 121 y ^ { 2 } } }$ .

A) $\frac { x ^ { 18 } } { 11 y }$
B) $\frac { x ^ { 9 } } { 11 }$
C) $\frac { x } { 11 y }$
D) $\frac { x ^ { 9 } } { 11 y }$
E) $\frac { x ^ { 9 } } { y }$

Question 34

Find the dimensions of a piece of carpet for a square classroom with $559$ square feet of floor space. Round your answer to two decimal places.

A) $23.64 \text { square feet }$
B) $23.64 \text { feet } \times 23.64 \text { feet }$
C) $23.64 \text { feet } \times 312,481 \text { feet }$
D) $312,481 \text { feet } \times 312,481 \text { feet }$
E) $23.64 \text { feet } \times 2 \text { feet }$

Question 35

Simplify the radical $\sqrt [ 3 ] { 189 }$ , if possible.

A) $3 \sqrt [ 3 ] { 7 }$
B) $3 \sqrt { 21 }$
C)3
D) $10 \sqrt { 3 }$
E) $6 \sqrt [ 3 ] { 7 }$

Question 36

Simplify the expression $\left( \frac { 9 m ^ { \frac { 1 } { 6 } } n ^ { \frac { 1 } { 3 } } } { 4 n ^ { \frac { 2 } { 3 } } } \right) ^ { 2 }$ .

A) $\frac { 9 m ^ { \frac { 1 } { 6 } } } { 4 n ^ { 2 } }$
B) $\frac { 81 m ^ { \frac { 1 } { 3 } } } { 16 n ^ { \frac { 2 } { 3 } } }$
C) $\frac { 81 m ^ { \frac { 1 } { 5 } } n ^ { \frac { 2 } { 3 } } } { 16 }$
D) $\frac { 9 m ^ { \frac { 1 } { 2 } } } { 4 n ^ { \frac { 2 } { 3 } } }$
E) $\frac { 81 m ^ { \frac { 1 } { 4 } } } { 16 n ^ { 2 } }$

Question 37

Simplify the expression $\frac { ( a - 6 ) ^ { \frac { 1 } { 7 } } } { \sqrt [ 7 ] { a - 6 } }$ .

A)1
B) -1
C) $( a - 6 ) ^ { \frac { 2 } { 7 } }$
D) $( a - 6 ) ^ { 6 }$
E) $\frac { 1 } { ( a - 6 ) ^ { \frac { 2 } { 7 } } }$

Question 38

Simplify $\frac { 30 - \sqrt { 81 } } { 3 }$ .

A)-3
B)10
C)21
D)1
E)7

Question 39

Use the formula $S = \sqrt { A }$ to find the length of the side s of a square whose area is A = 28.15 square inches. Round your answer to two decimal places.

A)149.35
B)792.42
C)5.31
D)28.15
E)-28.15

Question 40

Describe the domain of the function. $f ( x ) = \sqrt { - 3 x }$

A) $x \leq - 3$
B) $x \geq - 3$
C) $x \geq 0$
D) $x \leq 0$
E)all real numbers

Question 41

Combine the radical expression, if possible. $\sqrt { 36 x - 72 } + \sqrt { x - 2 }$

A) $6 \sqrt { 2 ( x - 2 ) }$
B) $8 \sqrt { x - 2 }$
C) $7 \sqrt { x - 2 }$
D) $7 \sqrt { 2 ( x - 2 ) }$
E) $6 \sqrt { x - 2 }$

Question 42

Simplify the expression $\sqrt { x } - \sqrt { 16 x }$ .

A) $- 3 \sqrt { x }$
B) $\sqrt { x }$
C) $- 3 x$
D) $17 \sqrt { x }$
E) $5 \sqrt { x }$

Question 43

Simplify the expression $3 \sqrt [ 3 ] { x } - 3 + \sqrt [ 3 ] { x } + 10$ .

A) $\sqrt [ 3 ] { x } + 7$
B) $4 \sqrt [ 3 ] { x } - 7$
C) $4 \sqrt [ 3 ] { x } + 7$
D) $7 \sqrt [ 3 ] { x } + 4$
E) $4 \sqrt { x }$

Question 44

Simplify the radical expression. $\sqrt [ 5 ] { \frac { - 243 x ^ { 2 } } { y ^ { 10 } } }$

A) $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$
B) $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 5 } }$
C) $\frac { 9 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$
D) $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$
E) $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$ .

Question 45

Simplify the expression $\sqrt { 64 x } + \sqrt { 9 x }$ .

A) $\sqrt { x }$
B) 67 $\sqrt { x }$
C) 11x
D) 11 $\sqrt { x }$
E) $\sqrt { 11 }$ x

Question 46

Simplify the expression $\sqrt { 3 } - 8 \sqrt { 7 } - 12 \sqrt { 3 }$ .

A) $- 11 \sqrt { 3 } - \sqrt { 7 }$
B) $11 \sqrt { 3 } - 8 \sqrt { 7 }$
C) $\sqrt { 3 } - 8 \sqrt { 7 }$
D) $- 11 \sqrt { 3 } - 8 \sqrt { 7 }$
E) $- 11 \sqrt { 3 } + 8 \sqrt { 7 }$

Question 47

Rationalize the denominator and simplify the expression $\sqrt [ 3 ] { \frac { 1 } { 512 y ^ { 2 } } }$ .

A) $\frac { 1 } { 8 y }$
B) $\frac { \sqrt [ 3 ] { y } } { 8 }$
C) $\frac { \sqrt [ 3 ] { y } } { 8 y }$
D) $\frac { \sqrt [ 3 ] { y } } { y }$
E) $\frac { \sqrt { y } } { 8 y }$

Question 48

Rationalize the denominator and simplify the expression $\frac { 2 } { \sqrt { z } }$ .

A) $\frac { 2 \sqrt { z } } { z ^ { 2 } }$
B) $\frac { 2 \sqrt { z } } { z }$
C) 2
D) $2 \sqrt { z }$
E) $\frac { 2 + \sqrt { z } } { z }$

Question 49

Combine the radical expression, if possible. $3 \sqrt { 125 } + 4 \sqrt { 20 }$

A) $13 \sqrt { 5 }$
B) $19 \sqrt { 5 }$
C) $23 \sqrt { 5 }$
D) $11 \sqrt { 5 }$
E) $17 \sqrt { 5 }$

Question 50

Combine the radical expression, if possible. $\sqrt { 16 x ^ { 9 } y ^ { 16 } } - 2 x ^ { 2 } y \sqrt [ 3 ] { 54 x ^ { 3 } y ^ { 13 } }$

A) $- 4 x ^ { 3 } y ^ { 5 } \sqrt [ 3 ] { 2 y }$
B) $- 7 x ^ { 4 } y ^ { 6 } \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 2 } }$
C) $8 x ^ { 3 } y ^ { 5 } \sqrt [ 5 ] { 3 x y }$
D) $7 x ^ { 4 } y ^ { 6 } \sqrt [ 3 ] { 3 y }$
E) $5 x ^ { 3 } y ^ { 5 } \sqrt [ 3 ] { 2 x y ^ { 2 } }$

Question 51

Choose the correct statement relating the two expressions.

A) $\sqrt { 7 } - \sqrt { 5 } \geq \sqrt { 7 - 5 }$
B) $\sqrt { 7 } - \sqrt { 5 } = \sqrt { 7 - 5 }$
C) $\sqrt { 7 } - \sqrt { 5 } < \sqrt { 7 - 5 }$
D) $\sqrt { 7 } - \sqrt { 5 } > \sqrt { 7 - 5 }$

Question 52

Perform the addition and simplify your answer. $\sqrt { \frac { 25 } { 3 x ^ { 3 } } } + \sqrt { 3 x ^ { 3 } }$

A) $\frac { \left( 5 + 3 x ^ { 3 } \right) \sqrt { 3 x } } { 3 x ^ { 2 } }$
B) $\frac { \left( 5 + 3 x ^ { 4 } \right) \sqrt { 3 x } } { 3 x ^ { 3 } }$
C) $\frac { \left( 5 + 3 x ^ { 2 } \right) 3 } { 3 x }$
D) $\frac { \left( 5 + 3 x ^ { 3 } \right) \sqrt { 3 x } } { 5 x ^ { 2 } }$
E) $\frac { \left( 3 + 5 x ^ { 2 } \right) \sqrt { 3 } } { 5 x }$

Question 53

Simplify the expression $9 \sqrt { u } - 3 + \sqrt { u } + 8$ .

A) $10 \sqrt { u } + 5$
B) $\sqrt { u } + 5$
C) $5 \sqrt { u } + 10$
D) $10 \sqrt { u } - 5$
E) $10 \sqrt { u }$

Question 54

Perform the subtraction and simplify your answer. $\sqrt { 80 } - \sqrt { \frac { 1 } { 5 } }$

A) $4 \sqrt { 5 }$
B) $\frac { 18 \sqrt { 5 } } { 5 }$
C) $5 \sqrt { 5 }$
D) $\frac { 21 \sqrt { 5 } } { 5 }$
E) $\frac { 19 \sqrt { 5 } } { 5 }$

Question 55

The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ gives the time t (seconds)for a pendulum of length L (in feet)to go through one complete cycle, both forward and back (its period). Find the period of the pendulum clock if the length is 2.25 feet. Round your answer to two decimal places.

A)1.67 seconds
B)0.83 second
C)0.27 second
D)0.44 second
E)0.79 second

Question 56

Rationalize the denominator and simplify further, if possible. $\sqrt { \frac { 64 } { x ^ { 3 } } }$

A) $\frac { 8 \sqrt { x } } { x ^ { 2 } }$
B) $\frac { 64 } { x ^ { 2 } }$
C) $\frac { 8 } { x ^ { 3 } }$
D) $\frac { 8 } { x ^ { 2 } }$
E) $\frac { 64 \sqrt { x } } { x }$

Question 57

Rationalize the denominator and simplify the expression $\frac { 3 } { \sqrt [ 3 ] { 4 } }$ .

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

Question 58

Enter the number 1.6 in your calculator and repeatedly take the square root. What number does the display appear to be approaching?

A)1
B)0
C)1.6
D)2.56
E)The display is not approaching a number.

Question 59

Simplify the expression $6 \sqrt { s t ^ { 3 } } - s \sqrt { s ^ { 3 } t }$ .

A) $\left( 6 t ^ { 2 } - s ^ { 2 } \right) \sqrt { s }$
B) $\left( 6 t - s ^ { 2 } \right) \sqrt { s t }$
C) $\left( 6 t ^ { 2 } - s \right) \sqrt { s t }$
D) $\left( 6 t ^ { 2 } + s ^ { 2 } \right) \sqrt { s t }$
E) $\left( 6 t ^ { 2 } - s ^ { 2 } \right) \sqrt { s t }$

Question 60

The four corners are cut from a 3-foot-by- 6-foot sheet of plywood, as shown in the figure. Find the perimeter of the remaining piece of plywood. In the figure $A = 6 , { B } = 3 \text { and } C = 1.5$ . Round your answer to two decimal places.

A)26.94 feet
B)10.24 feet
C)14.49 feet
D)21.94 feet
E)22.66 feet

Question 61

Find the product of $( \sqrt { t } - 6 )$ and its conjugate.

A) $\sqrt { t } - 6$
B) $t- 12$
C) $\sqrt { t } - 36$
D) $t - 36$
E) $t + 12 \sqrt { t } - 36$

Question 62

Multiply the expression by its conjugate and simplify. $\sqrt { 14 } - 10$

A) -86
B) 186
C) 96
D)1
E)0

Question 63

Multiply the expression by its conjugate and simplify. $8 \sqrt { 3 } + \sqrt { 4 }$

A) 48
B) 70
C) 188
D) 20
E) 572

Question 64

Complete the statement. $5 \sqrt { 98 } + 10 y \sqrt { 162 } = 5 \sqrt { 2 } ( \quad ? )$

A) $7 + 9 y$
B) $14 + 81 y$
C) $7 + 18 y$
D) $9 + 14 y$
E) $9 + 7 y$

Question 65

Multiply and simplify the expression. $\sqrt [ 3 ] { 2 } ( \sqrt [ 3 ] { 4 } + 4 )$

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

Question 66

Multiply and simplify. $( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

A) $2000 - 162 t$
B) $300 - 243 t$
C) $1000 + 91 t$
D) $200 + 81 t$
E) $100 - 729 t$

Question 67

The ratio of the width, w , of the Temple of Hephaestus to its height, h , is $\frac { w } { h } = \frac { 2 h } { \sqrt { 5 } - 1 }$ . This number is called the golden section. Early Greeks believed that the most aesthetically pleasing rectangle had this ratio. If the height is 5 , find the width. Rationalize the denominator and simplify the expression.

A) $\frac { 5 \sqrt { 5 } } { 2 }$
B) $\frac { \sqrt { 5 } + 5 } { 2 }$
C) $\frac { 5 \sqrt { 5 } - 5 } { 2 }$
D) $\frac { 5 \sqrt { 5 } + 5 } { 4 }$
E) $\frac { 5 \sqrt { 5 } + 5 } { 2 }$

Question 68

Simplify the expression $\frac { 5 } { \sqrt { 17 } - 3 }$ .

A) $\frac { 5 ( \sqrt { 17 } + 3 ) } { 280 }$
B) $\frac { 5 ( \sqrt { 17 } - 3 ) } { 26 }$
C) $\frac { 5 ( \sqrt { 17 } + 3 ) } { 26 }$
D) $\frac { 5 ( \sqrt { 17 } + 3 ) } { 8 }$
E) $\frac { 5 ( \sqrt { 17 } - 3 ) } { 8 }$

Question 69

Multiply and simplify. $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$

A) $27 y ^ { 3 } + 3 \sqrt { 49 y ^ { 2 } } - 49$
B) $3 y - 49$
C) $3 y - 7 \sqrt [ 3 ] { 3 y } + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49$
D) $27 y ^ { 3 } - 343$
E) $3 y - 7 \sqrt [ 3 ] { 9 y } - 343$

Question 70

Determine which value of x is a solution of $\sqrt { x } - 8 = 0$ .

A) x=128
B) x=8
C) x=0
D) x=-8
E) x=64

Question 71

Multiply and simplify. $( \sqrt [ 3 ] { t } + 1 ) \left( \sqrt [ 3 ] { t ^ { 2 } } + 8 \sqrt [ 3 ] { t } - 7 \right)$

A) $t + 9 \sqrt [ 3 ] { t ^ { 2 } } + \sqrt [ 3 ] { t } - 7$
B) $t + 10 \sqrt [ 3 ] { t ^ { 2 } } + 2 \sqrt [ 3 ] { t } - b$
C) $t + \sqrt [ 3 ] { t ^ { 2 } } + 7 \sqrt [ 3 ] { t } - 7$
D) $+ 7 \sqrt [ 3 ] { t ^ { 2 } } - 7$
E) $t + 8 \sqrt [ 3 ] { t ^ { 2 } } - 7 \sqrt [ 3 ] { t } - 7$

Question 72

Simplify the expression $\frac { 5 } { \sqrt { 5 } + \sqrt { 7 } }$ .

A) $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 2 }$
B) $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 12 }$
C) $- \frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 2 }$
D) $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 24 }$
E) $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 74 }$

Question 73

Rationalize the denominator of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$ and simplify.

A) $\sqrt { y }$
B) $\frac { 7 + y } { 49 - y }$
C) $\frac { 7 \sqrt { y } - y } { 49 - y }$
D) $\frac { 7 \sqrt { y } + y } { 49 + y }$
E) $\frac { 7 \sqrt { y } + y } { 49 - y }$

Question 74

Multiply and simplify. $\sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } )$

A) $7 \sqrt { 35 } + 5 \sqrt { 14 }$
B) $7 \sqrt { 5 } + 5 \sqrt { 7 }$
C) $7 \sqrt { 5 } + 5 \sqrt { 14 }$
D) $7 \sqrt { 10 } + 5 \sqrt { 14 }$
E) $7 \sqrt { 5 } + 5 \sqrt { 2 }$

Question 75

Rationalize the denominator of the expression and simplify. $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$

A) $\frac { 2 x + 15 \sqrt { x } - 4 } { 4 x - 7 }$
B) $\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }$
C) $\frac { x - \sqrt { x } - 28 } { 2 x - 49 }$
D) $\frac { x + 15 \sqrt { x } - 4 } { 2 x - 7 }$
E) $\frac { 2 x + 9 \sqrt { x } - 4 } { 4 x - 7 }$

Question 76

In the study of calculus, students sometimes rewrite an expression by rationalizing the numerator. Rationalize the numerator for the expression below. ( Note: The results will not be in simplest radical form.) $\frac { \sqrt { 11 } - \sqrt { 3 } } { 6 }$

A) $\frac { 56 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$
B) $\frac { 19 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$
C) $\frac { 7 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$
D) $\frac { 5 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$
E) $\frac { 4 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$

Question 77

Given $f ( x )$ below, evaluate $f ( 4 - \sqrt { 2 } )$ . $f ( x ) = x ^ { 2 } - 9 x + 5$

A) $- 13 + \sqrt { 2 }$
B) $- 31 + 10 \sqrt { 2 }$
C) $- 24 + 5 \sqrt { 2 }$
D) $- 17 + 17 \sqrt { 2 }$
E) $- 29 + 7 \sqrt { 2 }$

Question 78

Multiply and simplify. $( \sqrt { 13 } + 5 ) ( \sqrt { 5 } - 13 )$

A) $\sqrt { 65 } - 5 \sqrt { 5 } + 13 \sqrt { 13 } - 65$
B) $\sqrt { 65 } + 13 \sqrt { 5 } + 5 \sqrt { 13 } - 65$
C) $\sqrt { 65 } + 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$
D) $\sqrt { 65 } + 13 \sqrt { 5 } - 5 \sqrt { 13 } - 65$
E) $\sqrt { 65 } - 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$

Question 79

Multiply and simplify the expression $\sqrt { 5 } \sqrt { 21 }$ .

A) 105
B) $\sqrt { 105 }$
C) $\sqrt { 5 } + \sqrt { 21 }$
D) $\sqrt { 21 }$
E) $\sqrt { 5 }$

Question 80

Multiply and simplify. $( \sqrt { 3 } + 4 ) ( \sqrt { 3 } - 4 )$

A) 25
B) 1
C) -13
D) -7
E) 19