Question 1

Rationalize the denominator and simplify.
-$\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$

Accepted Answer

A)  $\frac { 1 } { 13 } ( \sqrt { 14 } + 1 )$ 
B)  $\frac { 1 } { 13 } ( \sqrt { 2 } + 1 )$ 
C)  $\frac { 1 } { 15 } ( \sqrt { 14 } + 1 )$ 
D)  $\frac { 1 } { 13 } ( \sqrt { 14 } - 1 )$ 
A)  $\frac { 1 } { 13 } ( \sqrt { 14 } + 1 )$ 
B)  $\frac { 1 } { 13 } ( \sqrt { 2 } + 1 )$ 
C)  $\frac { 1 } { 15 } ( \sqrt { 14 } + 1 )$ 
D)  $\frac { 1 } { 13 } ( \sqrt { 14 } - 1 )$

Question 2

Multiply the conjugates.
-$( \sqrt { 10 } + 4 ) ( \sqrt { 10 } - 4 )$

Accepted Answer

A)  26 
B)  6 
C)  $10 - 2 \sqrt { 4 }$ 
D)  $- 6$ 
A)  26 
B)  6 
C)  $10 - 2 \sqrt { 4 }$ 
D)  $- 6$

Question 3

Multiply the conjugates.
-$$( - 2 + 7 i ) ( - 2 - 7 i )$$

Accepted Answer

A)  $- 45$ 
B)  56 
C)  53 
D)  54 
A)  $- 45$ 
B)  56 
C)  53 
D)  54

Question 4

Add or subtract the complex numbers
-$$( 6 - 3 i ) + ( 7 + 9 i )$$

Accepted Answer

A)  $13 - 6 i$ 
B)  $13 + 6 i$ 
C)  $- 1 + 12 \mathrm { i }$ 
D)  $- 13 - 6 i$ 
A)  $13 - 6 i$ 
B)  $13 + 6 i$ 
C)  $- 1 + 12 \mathrm { i }$ 
D)  $- 13 - 6 i$

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { 216 }$$

Accepted Answer

A)  15 
B)  6 
C)  -6 
D) 36 
A)  15 
B)  6 
C)  -6 
D) 36

Question 6

Add or subtract. Assume all variables represent nonnegative real numbers.
-$5 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$

Accepted Answer

A)  $5 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$ 
B)  $8 \sqrt [ 3 ] { a }$ 
C)  $15 \sqrt [ 3 ] { a }$ 
D)  $6 \sqrt [ 3 ] { 27 a }$ 
A)  $5 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$ 
B)  $8 \sqrt [ 3 ] { a }$ 
C)  $15 \sqrt [ 3 ] { a }$ 
D)  $6 \sqrt [ 3 ] { 27 a }$

Question 7

Provide an appropriate response.
-If $\mathrm { n }$ is odd, under what condition is $\sqrt [ n ] { \mathrm { a } }$ negative?

Accepted Answer

A)  When a is negative 
B)  Never 
C)  When a is positive 
D)  When a is zero 
A)  When a is negative 
B)  Never 
C)  When a is positive 
D)  When a is zero

Question 8

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 3 } \cdot \sqrt { 27 }$

Accepted Answer

A)  9 
B)  162 
C)  81 
D)  18 
A)  9 
B)  162 
C)  81 
D)  18

Question 9

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt [ 3 ] { 6 } ( 5 \sqrt [ 3 ] { 6 } - \sqrt [ 3 ] { 36 } )$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 36 }$ 
B)  $5 \sqrt [ 3 ] { 6 } - 6 \sqrt [ 3 ] { 6 }$ 
C)  $5 \sqrt [ 3 ] { 36 } - 6$ 
D)  $5 \sqrt [ 3 ] { 6 } - 6$ 
A)  $4 \sqrt [ 3 ] { 36 }$ 
B)  $5 \sqrt [ 3 ] { 6 } - 6 \sqrt [ 3 ] { 6 }$ 
C)  $5 \sqrt [ 3 ] { 36 } - 6$ 
D)  $5 \sqrt [ 3 ] { 6 } - 6$

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 220 }$

Accepted Answer

A)  $- 2 \sqrt { 55 } \mathrm { i }$ 
B)  $2 \sqrt { 55 } \mathrm { i }$ 
C)  $2 \sqrt { 55 }$ 
D)  $- 2 \sqrt { 55 }$ 
A)  $- 2 \sqrt { 55 } \mathrm { i }$ 
B)  $2 \sqrt { 55 } \mathrm { i }$ 
C)  $2 \sqrt { 55 }$ 
D)  $- 2 \sqrt { 55 }$

Question 11

Multiply.
-$( 3 \sqrt { 3 } + 5 \sqrt { 5 } ) ^ { 2 }$

Accepted Answer

A)  $152 + 30 \sqrt { 15 }$ 
B)  152 
C)  $152 + 15 \sqrt { 15 }$ 
D)  $34 + 30 \sqrt { 15 }$ 
A)  $152 + 30 \sqrt { 15 }$ 
B)  152 
C)  $152 + 15 \sqrt { 15 }$ 
D)  $34 + 30 \sqrt { 15 }$

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt [ 3 ] { 384 }$

Accepted Answer

A)  19 
B)  $6 \sqrt [ 3 ] { 4 }$ 
C)  7 
D)  $4 \sqrt [ 3 ] { 6 }$ 
A)  19 
B)  $6 \sqrt [ 3 ] { 4 }$ 
C)  7 
D)  $4 \sqrt [ 3 ] { 6 }$

Question 13

Write the word or phrase that best completes each statement or answers the question.
-Explain why the expression cannot be simplified further. $$\sqrt [ 10 ] { a } - \sqrt [ 11 ] { a }$$

Accepted Answer

Indexes mu

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\frac { 2 } { 1 - \sqrt { 10 } }$ is to multiply both the numerator and denominator by $1 - \sqrt { 10 }$.

Accepted Answer

The statement is false. The easiest way

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { 12 }$

Accepted Answer

A)  $2 \sqrt { 3 }$ 
B)  2 
C)  $4 \sqrt { 3 }$ 
D)  3 
A)  $2 \sqrt { 3 }$ 
B)  2 
C)  $4 \sqrt { 3 }$ 
D)  3

Question 16

Add or subtract the complex numbers
-$$( 8 - 6 i ) + ( 9 + 2 i )$$

Accepted Answer

A)  $17 + 4 i$ 
B)  $- 17 + 4 i$ 
C)  $17 - 4 \mathrm { i }$ 
D)  $- 1 + 8 i$ 
A)  $17 + 4 i$ 
B)  $- 17 + 4 i$ 
C)  $17 - 4 \mathrm { i }$ 
D)  $- 1 + 8 i$

Question 17

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt { \frac { 25 } { 81 } }$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { 9 }$ 
B)  $\frac { \sqrt { 5 } } { \sqrt { 9 } }$ 
C)  $\frac { 5 } { 9 }$ 
D)  0 
A)  $\frac { \sqrt { 5 } } { 9 }$ 
B)  $\frac { \sqrt { 5 } } { \sqrt { 9 } }$ 
C)  $\frac { 5 } { 9 }$ 
D)  0

Question 18

Multiply the conjugates.
-$( \sqrt { 11 } - \sqrt { 3 } ) ( \sqrt { 11 } + \sqrt { 3 } )$

Accepted Answer

A)  $14 + 2 \sqrt { 33 }$ 
B)  $14 - 2 \sqrt { 33 }$ 
C)  14 
D)  8 
A)  $14 + 2 \sqrt { 33 }$ 
B)  $14 - 2 \sqrt { 33 }$ 
C)  14 
D)  8

Question 19

Simplify.
-$\frac { \mathrm { i } ^ { 30 } } { \mathrm { i } ^ { 28 } }$

Accepted Answer

A)  $- 1$ 
B)  $- \mathrm { i }$ 
C)  1 
D)  $i$ 
A)  $- 1$ 
B)  $- \mathrm { i }$ 
C)  1 
D)  $i$

Question 20

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 5 ] { x ^ { 2 } z ^ { 3 } } \cdot \sqrt [ 5 ] { x ^ { 13 } z ^ { 19 } }$$

Accepted Answer

A)  $x ^ { 4 } z ^ { 4 } \sqrt [ 5 ] { z }$ 
B)  $x ^ { 3 } z ^ { 4 } \sqrt [ 5 ] { z }$ 
C)  $x ^ { 4 } z ^ { 5 } \sqrt [ 5 ] { z ^ { 2 } }$ 
D)  $x ^ { 3 } z ^ { 4 } \sqrt [ 5 ] { z ^ { 2 } }$ 
A)  $x ^ { 4 } z ^ { 4 } \sqrt [ 5 ] { z }$ 
B)  $x ^ { 3 } z ^ { 4 } \sqrt [ 5 ] { z }$ 
C)  $x ^ { 4 } z ^ { 5 } \sqrt [ 5 ] { z ^ { 2 } }$ 
D)  $x ^ { 3 } z ^ { 4 } \sqrt [ 5 ] { z ^ { 2 } }$

Rationalize the denominator and simplify. - $\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }$

Multiply the conjugates. - $( \sqrt { 10 } + 4 ) ( \sqrt { 10 } - 4 )$

Multiply the conjugates. - $( - 2 + 7 i ) ( - 2 - 7 i )$

Add or subtract the complex numbers - $( 6 - 3 i ) + ( 7 + 9 i )$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { 216 }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $5 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$

Provide an appropriate response. -If $\mathrm { n }$ is odd, under what condition is $\sqrt [ n ] { \mathrm { a } }$ negative?

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 3 } \cdot \sqrt { 27 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { 6 } ( 5 \sqrt [ 3 ] { 6 } - \sqrt [ 3 ] { 36 } )$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 220 }$

Multiply. - $( 3 \sqrt { 3 } + 5 \sqrt { 5 } ) ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt [ 3 ] { 384 }$

Write the word or phrase that best completes each statement or answers the question. -Explain why the expression cannot be simplified further. $\sqrt [ 10 ] { a } - \sqrt [ 11 ] { a }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { 12 }$

Add or subtract the complex numbers - $( 8 - 6 i ) + ( 9 + 2 i )$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { \frac { 25 } { 81 } }$

Multiply the conjugates. - $( \sqrt { 11 } - \sqrt { 3 } ) ( \sqrt { 11 } + \sqrt { 3 } )$

Simplify. - $\frac { \mathrm { i } ^ { 30 } } { \mathrm { i } ^ { 28 } }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 5 ] { x ^ { 2 } z ^ { 3 } } \cdot \sqrt [ 5 ] { x ^ { 13 } z ^ { 19 } }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Radical Expressions and Equations

Rationalize the denominator and simplify. - 772−7\frac { \sqrt { 7 } } { 7 \sqrt { 2 } - \sqrt { 7 } }72​−7​7​​

Multiply the conjugates. - (10+4)(10−4)( \sqrt { 10 } + 4 ) ( \sqrt { 10 } - 4 )(10​+4)(10​−4)

Multiply the conjugates. - (−2+7i)(−2−7i)( - 2 + 7 i ) ( - 2 - 7 i )(−2+7i)(−2−7i)

Add or subtract the complex numbers - (6−3i)+(7+9i)( 6 - 3 i ) + ( 7 + 9 i )(6−3i)+(7+9i)

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 2163\sqrt [ 3 ] { 216 }3216​

Add or subtract. Assume all variables represent nonnegative real numbers. - 5a3+27a35 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }53a​+327a​

Provide an appropriate response. -If n\mathrm { n }n is odd, under what condition is an\sqrt [ n ] { \mathrm { a } }na​ negative?

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - 3⋅27\sqrt { 3 } \cdot \sqrt { 27 }3​⋅27​

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - 63(563−363)\sqrt [ 3 ] { 6 } ( 5 \sqrt [ 3 ] { 6 } - \sqrt [ 3 ] { 36 } )36​(536​−336​)

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - −220\sqrt { - 220 }−220​

Multiply. - (33+55)2( 3 \sqrt { 3 } + 5 \sqrt { 5 } ) ^ { 2 }(33​+55​)2

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - 3843\sqrt [ 3 ] { 384 }3384​

Write the word or phrase that best completes each statement or answers the question. -Explain why the expression cannot be simplified further. a10−a11\sqrt [ 10 ] { a } - \sqrt [ 11 ] { a }10a​−11a​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - 12\sqrt { 12 }12​

Add or subtract the complex numbers - (8−6i)+(9+2i)( 8 - 6 i ) + ( 9 + 2 i )(8−6i)+(9+2i)

Simplify the radical expression. Indicate if the expression is not a real number. - 2581\sqrt { \frac { 25 } { 81 } }8125​​

Multiply the conjugates. - (11−3)(11+3)( \sqrt { 11 } - \sqrt { 3 } ) ( \sqrt { 11 } + \sqrt { 3 } )(11​−3​)(11​+3​)

Simplify. - i30i28\frac { \mathrm { i } ^ { 30 } } { \mathrm { i } ^ { 28 } }i28i30​

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - x2z35⋅x13z195\sqrt [ 5 ] { x ^ { 2 } z ^ { 3 } } \cdot \sqrt [ 5 ] { x ^ { 13 } z ^ { 19 } }5x2z3​⋅5x13z19​