Question 1

Multiply the conjugates.
-$( 6 - 20 i ) ( 6 + 20 i )$

Accepted Answer

A)  $- 364$ 
B)  26 
C)  436 
D)  $- 14$ 
A)  $- 364$ 
B)  26 
C)  436 
D)  $- 14$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Accepted Answer

A)  $5 \sqrt [ 3 ] { 35 }$ 
B)  $10 \sqrt [ 3 ] { 35 }$ 
C)  $10 \sqrt [ 3 ] { 15 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$ 
A)  $5 \sqrt [ 3 ] { 35 }$ 
B)  $10 \sqrt [ 3 ] { 35 }$ 
C)  $10 \sqrt [ 3 ] { 15 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$

Question 3

Multiply.
-$( \sqrt { 2 } + \sqrt { 7 } ) ( \sqrt { 7 } + \sqrt { 5 } )$

Accepted Answer

A)  $\sqrt { 14 } + \sqrt { 10 } + 8 + \sqrt { 35 }$ 
B)  $\sqrt { 14 } + \sqrt { 10 } + \sqrt { 7 } + \sqrt { 35 }$ 
C)  $\sqrt { 14 } + \sqrt { 10 } + 7 + \sqrt { 35 }$ 
D)  $\sqrt { 14 } + \sqrt { 10 } + 49 + \sqrt { 35 }$ 
A)  $\sqrt { 14 } + \sqrt { 10 } + 8 + \sqrt { 35 }$ 
B)  $\sqrt { 14 } + \sqrt { 10 } + \sqrt { 7 } + \sqrt { 35 }$ 
C)  $\sqrt { 14 } + \sqrt { 10 } + 7 + \sqrt { 35 }$ 
D)  $\sqrt { 14 } + \sqrt { 10 } + 49 + \sqrt { 35 }$

Question 4

Rationalize the denominator and simplify.
-$$\frac { 3 - \sqrt { 2 } } { 3 + \sqrt { 2 } }$$

Accepted Answer

A)  $\frac { 7 + 6 \sqrt { 2 } } { 11 }$ 
B)  $\frac { 11 + 6 \sqrt { 2 } } { 7 }$ 
C)  $\frac { 7 - 6 \sqrt { 2 } } { 11 }$ 
D)  $\frac { 11 - 6 \sqrt { 2 } } { 7 }$ 
A)  $\frac { 7 + 6 \sqrt { 2 } } { 11 }$ 
B)  $\frac { 11 + 6 \sqrt { 2 } } { 7 }$ 
C)  $\frac { 7 - 6 \sqrt { 2 } } { 11 }$ 
D)  $\frac { 11 - 6 \sqrt { 2 } } { 7 }$

Question 5

Divide.
-$$( 9 - 8 i ) \div ( 5 - 8 i )$$

Accepted Answer

A)  $- \frac { 109 } { 39 } + \frac { 32 } { 39 } \mathrm { i }$ 
B)  $- \frac { 19 } { 89 } + \frac { 112 } { 89 } \mathrm { i }$ 
C)  $\frac { 109 } { 89 } + \frac { 32 } { 89 } \mathrm { i }$ 
D)  $\frac { 19 } { 39 } + \frac { 32 } { 39 } \mathrm { i }$ 
A)  $- \frac { 109 } { 39 } + \frac { 32 } { 39 } \mathrm { i }$ 
B)  $- \frac { 19 } { 89 } + \frac { 112 } { 89 } \mathrm { i }$ 
C)  $\frac { 109 } { 89 } + \frac { 32 } { 89 } \mathrm { i }$ 
D)  $\frac { 19 } { 39 } + \frac { 32 } { 39 } \mathrm { i }$

Question 6

Divide.
-$( 8 + 7 \mathrm { i } ) \div ( 9 - 8 \mathrm { i } )$

Accepted Answer

A)  $\frac { 16 } { 17 }$ 
B)  $\frac { 128 } { 17 } - \frac { 127 } { 17 } \mathrm { i }$ 
C)  $\frac { 128 } { 145 } + \frac { 1 } { 145 } \mathrm { i }$ 
D)  $\frac { 16 } { 145 } + \frac { 127 } { 145 }$ i 
A)  $\frac { 16 } { 17 }$ 
B)  $\frac { 128 } { 17 } - \frac { 127 } { 17 } \mathrm { i }$ 
C)  $\frac { 128 } { 145 } + \frac { 1 } { 145 } \mathrm { i }$ 
D)  $\frac { 16 } { 145 } + \frac { 127 } { 145 }$ i

Question 7

Evaluate the radical function at the given value of the variable.
-$$g ( x ) = \sqrt { 3 x ^ { 2 } + 9 }$$

Accepted Answer

A)  $[ - 3 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 0 , \infty )$ 
A)  $[ - 3 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ 0 , \infty )$

Question 8

Evaluate the radical function at the given value of the variable.
-$$f ( x ) = \sqrt { 2 - 4 x }$$

Accepted Answer

A)  $\left( - \infty , \frac { 1 } { 2 } \right)$ 
B)  $\left( - \infty , \frac { 1 } { 2 } \right]$ 
C)  $\left[ - \frac { 1 } { 2 } , \infty \right)$ 
D)  $\left[ \frac { 1 } { 2 } , \infty \right)$ 
A)  $\left( - \infty , \frac { 1 } { 2 } \right)$ 
B)  $\left( - \infty , \frac { 1 } { 2 } \right]$ 
C)  $\left[ - \frac { 1 } { 2 } , \infty \right)$ 
D)  $\left[ \frac { 1 } { 2 } , \infty \right)$

Question 9

Multiply the conjugates.
-$$( 5 - 2 i ) ( 5 + 2 i )$$

Accepted Answer

A)  $25 + 4 \mathrm { i }$ 
B)  29 
C)  21 
D)  $25 - 4 \mathrm { i }$ 
A)  $25 + 4 \mathrm { i }$ 
B)  29 
C)  21 
D)  $25 - 4 \mathrm { i }$

Question 10

Provide an appropriate response.
-If $\mathrm { a } < 0$, which of the following correctly describes $- \sqrt { - a }$ ?

Accepted Answer

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

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain how to evaluate $( - 64 ) ^ { 5 / 3 }$

Accepted Answer

Answers may vary. One possibil

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain why the equation $x ^ { 2 } = 64$ has two real-number solutions, while the equation $\sqrt { \mathrm { x } } = 8$ has only one real number solution.

Accepted Answer

Answers may vary. One possibility: Takin

Question 13

Add or subtract.
-$\sqrt { 2 } + 5 \sqrt { 98 } + 4 \sqrt { 200 }$

Accepted Answer

A)  $9 \sqrt { 300 }$ 
B)  $76 \sqrt { 2 }$ 
C)  $9 \sqrt { 2 }$ 
D)  $76 \sqrt { 300 }$ 
A)  $9 \sqrt { 300 }$ 
B)  $76 \sqrt { 2 }$ 
C)  $9 \sqrt { 2 }$ 
D)  $76 \sqrt { 300 }$

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$- \sqrt { - 252 }$

Accepted Answer

A)  $6 \sqrt { 7 } \mathrm { i }$ 
B)  $6 \sqrt { 7 }$ 
C)  $- 6 \sqrt { 7 }$ 
D)  $- 6 \sqrt { 7 } i$ 
A)  $6 \sqrt { 7 } \mathrm { i }$ 
B)  $6 \sqrt { 7 }$ 
C)  $- 6 \sqrt { 7 }$ 
D)  $- 6 \sqrt { 7 } i$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$$\sqrt { - 1600 }$$

Accepted Answer

A)  $40 \mathrm { i }$ 
B)  $- 40 \mathrm { i }$ 
C)  $\pm 40$ 
D)  i $\sqrt { 40 }$ 
A)  $40 \mathrm { i }$ 
B)  $- 40 \mathrm { i }$ 
C)  $\pm 40$ 
D)  i $\sqrt { 40 }$

Question 16

Multiply. Write your answer in a + bi form.
-$$( 8 + 5 i ) ( 6 - 4 i )$$

Accepted Answer

A)  $- 20 i ^ { 2 } - 2 i + 48$ 
B)  $68 - 2 \mathrm { i }$ 
C)  $68 + 2 i$ 
D)  $28 + 62 \mathrm { i }$ 
A)  $- 20 i ^ { 2 } - 2 i + 48$ 
B)  $68 - 2 \mathrm { i }$ 
C)  $68 + 2 i$ 
D)  $28 + 62 \mathrm { i }$

Question 17

Find the missing complex number.
-(-2 + i) + ? = 8 + 3i

Accepted Answer

A)  10 + 2i 
B)  10 - 2i 
C)  -10 - 2i 
D)  6 + 4i 
A)  10 + 2i 
B)  10 - 2i 
C)  -10 - 2i 
D)  6 + 4i

Question 18

Simplify.
-$\sqrt [ 3 ] { 9 } \cdot \sqrt [ 3 ] { 3 }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 3 }$ 
B)  5 
C)  3 
D)  $\sqrt [ 3 ] { 27 }$ 
A)  $3 \sqrt [ 3 ] { 3 }$ 
B)  5 
C)  3 
D)  $\sqrt [ 3 ] { 27 }$

Question 19

Multiply the conjugates.
-$( \sqrt { 3 } + 1 ) ( \sqrt { 3 } - 1 )$

Accepted Answer

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

Question 20

Solve the problem.
-A manufacturerʹs cost is given by $$C = 400 \sqrt [ 3 ] { n } + 200$$

Accepted Answer

A)  $1000 
B)  $1800 
C)  $100 
D)  $3400 
A)  $1000 
B)  $1800 
C)  $100 
D)  $3400

Multiply the conjugates. - $( 6 - 20 i ) ( 6 + 20 i )$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Multiply. - $( \sqrt { 2 } + \sqrt { 7 } ) ( \sqrt { 7 } + \sqrt { 5 } )$

Rationalize the denominator and simplify. - $\frac { 3 - \sqrt { 2 } } { 3 + \sqrt { 2 } }$

Divide. - $( 9 - 8 i ) \div ( 5 - 8 i )$

Divide. - $( 8 + 7 \mathrm { i } ) \div ( 9 - 8 \mathrm { i } )$

Evaluate the radical function at the given value of the variable. - $g ( x ) = \sqrt { 3 x ^ { 2 } + 9 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { 2 - 4 x }$

Multiply the conjugates. - $( 5 - 2 i ) ( 5 + 2 i )$

Provide an appropriate response. -If $\mathrm { a } < 0$ , which of the following correctly describes $- \sqrt { - a }$ ?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain how to evaluate $( - 64 ) ^ { 5 / 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain why the equation $x ^ { 2 } = 64$ has two real-number solutions, while the equation $\sqrt { \mathrm { x } } = 8$ has only one real number solution.

Add or subtract. - $\sqrt { 2 } + 5 \sqrt { 98 } + 4 \sqrt { 200 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $- \sqrt { - 252 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 1600 }$

Multiply. Write your answer in a + bi form. - $( 8 + 5 i ) ( 6 - 4 i )$

Find the missing complex number. -(-2 + i) + ? = 8 + 3i

Simplify. - $\sqrt [ 3 ] { 9 } \cdot \sqrt [ 3 ] { 3 }$

Multiply the conjugates. - $( \sqrt { 3 } + 1 ) ( \sqrt { 3 } - 1 )$

Solve the problem. -A manufacturerʹs cost is given by $C = 400 \sqrt [ 3 ] { n } + 200$

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

Multiply the conjugates. - (6−20i)(6+20i)( 6 - 20 i ) ( 6 + 20 i )(6−20i)(6+20i)

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - 1753⋅253\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }3175​⋅325​

Multiply. - (2+7)(7+5)( \sqrt { 2 } + \sqrt { 7 } ) ( \sqrt { 7 } + \sqrt { 5 } )(2​+7​)(7​+5​)

Rationalize the denominator and simplify. - 3−23+2\frac { 3 - \sqrt { 2 } } { 3 + \sqrt { 2 } }3+2​3−2​​

Divide. - (9−8i)÷(5−8i)( 9 - 8 i ) \div ( 5 - 8 i )(9−8i)÷(5−8i)

Divide. - (8+7i)÷(9−8i)( 8 + 7 \mathrm { i } ) \div ( 9 - 8 \mathrm { i } )(8+7i)÷(9−8i)

Evaluate the radical function at the given value of the variable. - g(x)=3x2+9g ( x ) = \sqrt { 3 x ^ { 2 } + 9 }g(x)=3x2+9​

Evaluate the radical function at the given value of the variable. - f(x)=2−4xf ( x ) = \sqrt { 2 - 4 x }f(x)=2−4x​

Multiply the conjugates. - (5−2i)(5+2i)( 5 - 2 i ) ( 5 + 2 i )(5−2i)(5+2i)

Provide an appropriate response. -If a<0\mathrm { a } < 0a<0 , which of the following correctly describes −−a- \sqrt { - a }−−a​ ?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain how to evaluate (−64)5/3( - 64 ) ^ { 5 / 3 }(−64)5/3

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain why the equation x2=64x ^ { 2 } = 64x2=64 has two real-number solutions, while the equation x=8\sqrt { \mathrm { x } } = 8x​=8 has only one real number solution.

Add or subtract. - 2+598+4200\sqrt { 2 } + 5 \sqrt { 98 } + 4 \sqrt { 200 }2​+598​+4200​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - −−252- \sqrt { - 252 }−−252​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - −1600\sqrt { - 1600 }−1600​

Multiply. Write your answer in a + bi form. - (8+5i)(6−4i)( 8 + 5 i ) ( 6 - 4 i )(8+5i)(6−4i)