Question 1

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

Accepted Answer

A)  2 - 9i 
B)  2 - 7i 
C)  -2 + 7i 
D)  -2 + 9i 
A)  2 - 9i 
B)  2 - 7i 
C)  -2 + 7i 
D)  -2 + 9i

Question 2

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$6 \sqrt { 5 x } ( \sqrt { 11 } + \sqrt { 5 x } )$

Accepted Answer

A)  $6 \sqrt { 11 } + 5 x$ 
B)  $6 \sqrt { 55 } + 5 x$ 
C)  $6 \sqrt { 55 x } + 30 x$ 
D)  $30 \sqrt { 11 x } + 30 x$ 
A)  $6 \sqrt { 11 } + 5 x$ 
B)  $6 \sqrt { 55 } + 5 x$ 
C)  $6 \sqrt { 55 x } + 30 x$ 
D)  $30 \sqrt { 11 x } + 30 x$

Question 3

Divide.
-$( - 13 - 10 i ) \div ( 7 \mathrm { i } )$

Accepted Answer

A)  $\frac { 10 } { 7 } + \frac { 13 } { 7 } \mathrm { i }$ 
B)  $\frac { 10 } { 7 } - \frac { 13 } { 7 } \mathrm { i }$ 
C)  $- \frac { 10 } { 7 } - \frac { 13 } { 7 } \mathrm { i }$ 
D)  $- \frac { 10 } { 7 } + \frac { 13 } { 7 } \mathrm { i }$ 
A)  $\frac { 10 } { 7 } + \frac { 13 } { 7 } \mathrm { i }$ 
B)  $\frac { 10 } { 7 } - \frac { 13 } { 7 } \mathrm { i }$ 
C)  $- \frac { 10 } { 7 } - \frac { 13 } { 7 } \mathrm { i }$ 
D)  $- \frac { 10 } { 7 } + \frac { 13 } { 7 } \mathrm { i }$

Question 4

Find the missing complex number.
-(2 + i)(?) = 7 + 6i

Accepted Answer

A)  45 + 65 i 
B) 23 + 13 i 
C) 2- 1 
D) 4 + i 
A)  45 + 65 i 
B) 23 + 13 i 
C) 2- 1 
D) 4 + i

Question 5

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt { ( b + 2 ) ^ { 2 } }$

Accepted Answer

A)  $| b + 2 |$ 
B)  $\sqrt { \mathrm { b } } + 2$ 
C)  $| b - 2 |$ 
D)  $\mathrm { b } + 4$ 
A)  $| b + 2 |$ 
B)  $\sqrt { \mathrm { b } } + 2$ 
C)  $| b - 2 |$ 
D)  $\mathrm { b } + 4$

Question 6

Find the missing complex number.
-(8 + 5i) - ? = 10 + 4i

Accepted Answer

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

Question 7

Provide an appropriate response.(True or false)
-If a > 0, $\text { then } \frac { a } { i } = i a$

Accepted Answer

A) True 
 B)False

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 172 }$

Accepted Answer

A)  $- 2 \sqrt { 43 }$ 
B)  $2 \sqrt { 43 } \mathrm { i }$ 
C)  $- 2 \sqrt { 43 } \mathrm { i }$ 
D)  $2 \sqrt { 43 }$ 
A)  $- 2 \sqrt { 43 }$ 
B)  $2 \sqrt { 43 } \mathrm { i }$ 
C)  $- 2 \sqrt { 43 } \mathrm { i }$ 
D)  $2 \sqrt { 43 }$

Question 9

Evaluate the radical function at the given value of the variable.
-$$f ( x ) = \sqrt [ 3 ] { x - 3 }$$

Accepted Answer

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

Question 10

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 15 } \cdot \sqrt { 12 }$

Accepted Answer

A)  $- 10 \sqrt { 3 }$ 
B)  $6 \sqrt { 5 }$ 
C)  $- 6 \sqrt { 5 }$ 
D)  $10 \sqrt { 3 }$ 
A)  $- 10 \sqrt { 3 }$ 
B)  $6 \sqrt { 5 }$ 
C)  $- 6 \sqrt { 5 }$ 
D)  $10 \sqrt { 3 }$

Question 11

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt { \frac { 441 } { 289 } }$

Accepted Answer

A)  $\frac { 220 } { 144 }$ 
B)  $\frac { 21 } { 18 }$ 
C)  $\frac { 21 } { 17 }$ 
D)  $\frac { 22 } { 17 }$ 
A)  $\frac { 220 } { 144 }$ 
B)  $\frac { 21 } { 18 }$ 
C)  $\frac { 21 } { 17 }$ 
D)  $\frac { 22 } { 17 }$

Question 12

Provide an appropriate response.
-$\sqrt [ 4 ] { 3 } \cdot \sqrt [ 5 ] { 2 }$

Accepted Answer

A)  $\sqrt [ 20 ] { 259 }$ 
B)  $\sqrt [ 20 ] { 6 }$ 
C)  $\sqrt [ 20 ] { 3888 }$ 
D)  $\sqrt [ 9 ] { 3888 }$ 
A)  $\sqrt [ 20 ] { 259 }$ 
B)  $\sqrt [ 20 ] { 6 }$ 
C)  $\sqrt [ 20 ] { 3888 }$ 
D)  $\sqrt [ 9 ] { 3888 }$

Question 13

Multiply.
-10i ∙ 7i

Accepted Answer

A)  -17 
B)  70 
C)  -70 
D)  17 
A)  -17 
B)  70 
C)  -70 
D)  17

Question 14

Evaluate the radical function at the given value of the variable.
-$$f ( x ) = \sqrt { 4 x + 9 }$$

Accepted Answer

A)  $\left( \frac { 9 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 9 } { 4 } , \infty \right)$ 
C)  $\left[ - \frac { 9 } { 4 } , \infty \right]$ 
D)  $\left( - \infty , - \frac { 9 } { 4 } \right)$ 
A)  $\left( \frac { 9 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 9 } { 4 } , \infty \right)$ 
C)  $\left[ - \frac { 9 } { 4 } , \infty \right]$ 
D)  $\left( - \infty , - \frac { 9 } { 4 } \right)$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 2 } ( \sqrt { 2 } - \sqrt { 14 } )$

Accepted Answer

A)  $2 - \sqrt { 28 }$ 
B)  $2 + 2 \sqrt { 7 }$ 
C)  $2 - 2 \sqrt { 7 }$ 
D)  $2 - 7 \sqrt { 2 }$ 
A)  $2 - \sqrt { 28 }$ 
B)  $2 + 2 \sqrt { 7 }$ 
C)  $2 - 2 \sqrt { 7 }$ 
D)  $2 - 7 \sqrt { 2 }$

Question 16

Add or subtract.
-$4 \sqrt { 14 } + 17 \sqrt { 14 }$

Accepted Answer

A)  $14 \sqrt { 14 }$ 
B)  $- 22 \sqrt { 14 }$ 
C)  $- 13 \sqrt { 14 }$ 
D)  $21 \sqrt { 14 }$ 
A)  $14 \sqrt { 14 }$ 
B)  $- 22 \sqrt { 14 }$ 
C)  $- 13 \sqrt { 14 }$ 
D)  $21 \sqrt { 14 }$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain what is wrong with this first step in the solution process for the equation $$\sqrt { 2 x + 7 } = \sqrt { - 9 x - 5 } \cdot 2 x + 7 = 9 x + 5$$

Accepted Answer

The squaring of the

Question 18

Solve. Check for extraneous solutions.
-$$( x + 1 ) ^ { 1 / 3 } = 4$$

Accepted Answer

A)  $\{ 63 \}$ 
B)  $\{ 64 \}$ 
C)  $\{ 15 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 63 \}$ 
B)  $\{ 64 \}$ 
C)  $\{ 15 \}$ 
D)  $\{ 3 \}$

Question 19

Find the missing number.
-$$\sqrt { ? } = 11 y ^ { 3 }$$

Accepted Answer

A)  $121 y ^ { 3 }$ 
B)  $11 y ^ { 3 }$ 
C)  $121 y ^ { 6 }$ 
D)  $11 \mathrm { y } ^ { 6 }$ 
A)  $121 y ^ { 3 }$ 
B)  $11 y ^ { 3 }$ 
C)  $121 y ^ { 6 }$ 
D)  $11 \mathrm { y } ^ { 6 }$

Question 20

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$4 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )$

Accepted Answer

A)  $28 \sqrt { 11 } + 28$ 
B)  $4 \sqrt { 11 } + 7$ 
C)  $4 \sqrt { 77 } + 28$ 
D)  $4 \sqrt { 77 } + 7$ 
A)  $28 \sqrt { 11 } + 28$ 
B)  $4 \sqrt { 11 } + 7$ 
C)  $4 \sqrt { 77 } + 28$ 
D)  $4 \sqrt { 77 } + 7$

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

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $6 \sqrt { 5 x } ( \sqrt { 11 } + \sqrt { 5 x } )$

Divide. - $( - 13 - 10 i ) \div ( 7 \mathrm { i } )$

Find the missing complex number. -(2 + i)(?) = 7 + 6i

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { ( b + 2 ) ^ { 2 } }$

Find the missing complex number. -(8 + 5i) - ? = 10 + 4i

Provide an appropriate response.(True or false) -If a > 0, $\text { then } \frac { a } { i } = i a$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 172 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt [ 3 ] { x - 3 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 15 } \cdot \sqrt { 12 }$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { \frac { 441 } { 289 } }$

Provide an appropriate response. - $\sqrt [ 4 ] { 3 } \cdot \sqrt [ 5 ] { 2 }$

Multiply. -10i ∙ 7i

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { 4 x + 9 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 2 } ( \sqrt { 2 } - \sqrt { 14 } )$

Add or subtract. - $4 \sqrt { 14 } + 17 \sqrt { 14 }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain what is wrong with this first step in the solution process for the equation $\sqrt { 2 x + 7 } = \sqrt { - 9 x - 5 } \cdot 2 x + 7 = 9 x + 5$

Solve. Check for extraneous solutions. - $( x + 1 ) ^ { 1 / 3 } = 4$

Find the missing number. - $\sqrt { ? } = 11 y ^ { 3 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $4 \sqrt { 7 } ( \sqrt { 11 } + \sqrt { 7 } )$

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

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

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - 65x(11+5x)6 \sqrt { 5 x } ( \sqrt { 11 } + \sqrt { 5 x } )65x​(11​+5x​)

Divide. - (−13−10i)÷(7i)( - 13 - 10 i ) \div ( 7 \mathrm { i } )(−13−10i)÷(7i)