Question 1

Simplify. Assume all variables represent nonnegative values.
-$\sqrt { \frac { 5 } { r ^ { 4 } } }$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { \sqrt { r ^ { 4 } } }$ 
B)  $\frac { \sqrt { 5 r ^ { 4 } } } { r ^ { 4 } }$ 
C)  $\frac { \sqrt { 5 } } { r ^ { 2 } }$ 
D)  $\frac { \sqrt { 5 } } { \mathrm { r } }$ 
A)  $\frac { \sqrt { 5 } } { \sqrt { r ^ { 4 } } }$ 
B)  $\frac { \sqrt { 5 r ^ { 4 } } } { r ^ { 4 } }$ 
C)  $\frac { \sqrt { 5 } } { r ^ { 2 } }$ 
D)  $\frac { \sqrt { 5 } } { \mathrm { r } }$

Question 2

Multiply the conjugates.
-(13 - 9i)(13 + 9i)

Accepted Answer

A)  4 
B)  22 
C)  250 
D)  88 
A)  4 
B)  22 
C)  250 
D)  88

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 324 }$

Accepted Answer

A)  $\pm 18$ 
B)  $- \mathrm { i } \sqrt { 18 }$ 
C)  $- 18 \mathrm { i }$ 
D)  $18 \mathrm { i }$ 
A)  $\pm 18$ 
B)  $- \mathrm { i } \sqrt { 18 }$ 
C)  $- 18 \mathrm { i }$ 
D)  $18 \mathrm { i }$

Question 4

Find the missing complex number.
-(7 + 8i) - ? = 15 + 7i

Accepted Answer

A)  -8 + i 
B) 15 - 7i 
C)  -15 - 7i 
D)  -8 - i 
A)  -8 + i 
B) 15 - 7i 
C)  -15 - 7i 
D)  -8 - i

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 49 }$

Accepted Answer

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

Question 6

Solve the problem.
-For the function $f ( x ) = 5 \sqrt { 2 x - 8 } - 5 \sqrt { x + 5 }$, find all values $x$ for which $f ( x ) = - 15$.

Accepted Answer

A)  4 
B)  15 
C)  9 
D)  $- 9$ 
A)  4 
B)  15 
C)  9 
D)  $- 9$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 294 }$

Accepted Answer

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

Question 8

Add or subtract the complex numbers
-(3 + 5i) - (6 + 10i) - (4 - 3i)

Accepted Answer

A)  -7 + 12i 
B)  13 + 12i 
C)  13 - 2i 
D)  -7 - 2i 
A)  -7 + 12i 
B)  13 + 12i 
C)  13 - 2i 
D)  -7 - 2i

Question 9

Provide an appropriate response.(True or false)
-i = -1

Accepted Answer

A) True 
 B)False

Question 10

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x } \left( \sqrt [ 3 ] { x ^ { 2 } } - \sqrt [ 3 ] { 24 x ^ { 2 } } \right)$$

Accepted Answer

A)  $x - 2 x \sqrt [ 3 ] { 3 }$ 
B)  $x - 8 x \sqrt [ 3 ] { 3 }$ 
C)  $x - 2 x ^ { 3 } \sqrt [ 3 ] { 3 }$ 
D)  $x - 6 x$ 
A)  $x - 2 x \sqrt [ 3 ] { 3 }$ 
B)  $x - 8 x \sqrt [ 3 ] { 3 }$ 
C)  $x - 2 x ^ { 3 } \sqrt [ 3 ] { 3 }$ 
D)  $x - 6 x$

Question 11

Find the missing number.
-$$\sqrt { ? } = 6 x$$

Accepted Answer

A)  $36 x ^ { 2 }$ 
B)  $- 6 x$ 
C)  $36 x$ 
D)  $6 x ^ { 2 }$ 
A)  $36 x ^ { 2 }$ 
B)  $- 6 x$ 
C)  $36 x$ 
D)  $6 x ^ { 2 }$

Question 12

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt { x ^ { 10 } }$

Accepted Answer

A)  $\left| x ^ { 5 } \right|$ 
B)  $x ^ { 5 }$ 
C)  $- \mathrm { x } ^ { 5 }$ 
D)  $- \left| x ^ { 5 } \right|$ 
A)  $\left| x ^ { 5 } \right|$ 
B)  $x ^ { 5 }$ 
C)  $- \mathrm { x } ^ { 5 }$ 
D)  $- \left| x ^ { 5 } \right|$

Question 13

Provide an appropriate response.
-Can the sum be simplified without first simplifying the individual radical expressions? $$2 \sqrt [ 12 ] { 2 } - 9 \sqrt [ 12 ] { 2 }$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 14

Simplify.
-$\mathrm{i}^{29} \cdot \mathrm{i} ^{27}$

Accepted Answer

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

Question 15

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt { 200 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Accepted Answer

A)  $10 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$ 
B)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
C)  $10 \mathrm { k } ^ { 2 } q ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
D)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
A)  $10 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$ 
B)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
C)  $10 \mathrm { k } ^ { 2 } q ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
D)  $10 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$

Question 16

Provide an appropriate response.
-How many real cube roots does any positive number have?

Accepted Answer

A)  Three 
B)  None 
C)  One 
D)  Two 
A)  Three 
B)  None 
C)  One 
D)  Two

Question 17

Provide an appropriate response.
-Can the following be simplified to an expression involving a single radical? $$x \sqrt [ 3 ] { 135 } + \sqrt [ 3 ] { 2560 x ^ { 3 } }$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 18

Divide.
-$$- 7 \mathrm { i } \div ( - 2 + 8 \mathrm { i } )$$

Accepted Answer

A)  $\frac { 14 } { 15 } - \frac { 7 } { 30 } \mathrm { i }$ 
B)  $\frac { 14 } { 17 } + \frac { 7 } { 34 } \mathrm { i }$ 
C)  $- \frac { 14 } { 17 } + \frac { 7 } { 34 } \mathrm { i }$ 
D)  $- \frac { 14 } { 15 } - \frac { 7 } { 30 } \mathrm { i }$ 
A)  $\frac { 14 } { 15 } - \frac { 7 } { 30 } \mathrm { i }$ 
B)  $\frac { 14 } { 17 } + \frac { 7 } { 34 } \mathrm { i }$ 
C)  $- \frac { 14 } { 17 } + \frac { 7 } { 34 } \mathrm { i }$ 
D)  $- \frac { 14 } { 15 } - \frac { 7 } { 30 } \mathrm { i }$

Question 19

Multiply. Write your answer in a + bi form.
-$$( 6 - 2 i ) ^ { 2 }$$

Accepted Answer

A)  $40 - 24 i$ 
B)  $36 - 20 \mathrm { i }$ 
C)  $36 - 28 \mathrm { i }$ 
D)  $32 - 24 i$ 
A)  $40 - 24 i$ 
B)  $36 - 20 \mathrm { i }$ 
C)  $36 - 28 \mathrm { i }$ 
D)  $32 - 24 i$

Question 20

Multiply.
-$\sqrt { - 36 } \cdot \sqrt { - 9 }$

Accepted Answer

A)  18 
B)  $- 18$ 
C)  $- 18 \mathrm { i }$ 
D)  $18 \mathrm { i }$ 
A)  18 
B)  $- 18$ 
C)  $- 18 \mathrm { i }$ 
D)  $18 \mathrm { i }$

Simplify. Assume all variables represent nonnegative values. - $\sqrt { \frac { 5 } { r ^ { 4 } } }$

Multiply the conjugates. -(13 - 9i)(13 + 9i)

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 324 }$

Find the missing complex number. -(7 + 8i) - ? = 15 + 7i

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 49 }$

Solve the problem. -For the function $f ( x ) = 5 \sqrt { 2 x - 8 } - 5 \sqrt { x + 5 }$ , find all values $x$ for which $f ( x ) = - 15$ .

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 294 }$

Add or subtract the complex numbers -(3 + 5i) - (6 + 10i) - (4 - 3i)

Provide an appropriate response.(True or false) -i = -1

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { x } \left( \sqrt [ 3 ] { x ^ { 2 } } - \sqrt [ 3 ] { 24 x ^ { 2 } } \right)$

Find the missing number. - $\sqrt { ? } = 6 x$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { x ^ { 10 } }$

Provide an appropriate response. -Can the sum be simplified without first simplifying the individual radical expressions? $2 \sqrt [ 12 ] { 2 } - 9 \sqrt [ 12 ] { 2 }$

Simplify. - $\mathrm{i}^{29} \cdot \mathrm{i} ^{27}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt { 200 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Provide an appropriate response. -How many real cube roots does any positive number have?

Provide an appropriate response. -Can the following be simplified to an expression involving a single radical? $x \sqrt [ 3 ] { 135 } + \sqrt [ 3 ] { 2560 x ^ { 3 } }$

Divide. - $- 7 \mathrm { i } \div ( - 2 + 8 \mathrm { i } )$

Multiply. Write your answer in a + bi form. - $( 6 - 2 i ) ^ { 2 }$

Multiply. - $\sqrt { - 36 } \cdot \sqrt { - 9 }$

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

Simplify. Assume all variables represent nonnegative values. - 5r4\sqrt { \frac { 5 } { r ^ { 4 } } }r45​​