Question 1

Find the missing complex number.
-(4 - 2i) + ? = 7 + 3i

Accepted Answer

A)  -7 - 3i 
B)  3 + 5i 
C)  1 + 7i 
D)  7 - 3i 
A)  -7 - 3i 
B)  3 + 5i 
C)  1 + 7i 
D)  7 - 3i

Question 2

Solve the problem.
-For the function $f ( x ) = \sqrt [ 3 ] { 6 x + 6 } + 4$, find all values $x$ for which $f ( x ) = 8$

Accepted Answer

A)  $9 \frac { 2 } { 3 }$ 
B)  $\sqrt [ 3 ] { 54 }$ 
C)  $1 \frac { 2 } { 3 }$ 
D)  $83 \frac { 2 } { 3 }$ 
A)  $9 \frac { 2 } { 3 }$ 
B)  $\sqrt [ 3 ] { 54 }$ 
C)  $1 \frac { 2 } { 3 }$ 
D)  $83 \frac { 2 } { 3 }$

Question 3

Rationalize the denominator and simplify.
-$\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }$

Accepted Answer

A)  $\frac { 59 \sqrt { 21 } + 928 } { 727 }$ 
B)  $\frac { 59 \sqrt { 21 } + 6 \sqrt { 3 } + 130 \sqrt { 7 } } { 673 }$ 
C)  $\frac { 2167 } { 727 }$ 
D)  $\frac { 59 \sqrt { 21 } + 928 } { 673 }$ 
A)  $\frac { 59 \sqrt { 21 } + 928 } { 727 }$ 
B)  $\frac { 59 \sqrt { 21 } + 6 \sqrt { 3 } + 130 \sqrt { 7 } } { 673 }$ 
C)  $\frac { 2167 } { 727 }$ 
D)  $\frac { 59 \sqrt { 21 } + 928 } { 673 }$

Question 4

Add or subtract. Assume all variables represent nonnegative real numbers.
-$$6 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }$$

Accepted Answer

A)  $x \sqrt [ 11 ] { x y }$ 
B)  $2 x \sqrt [ 11 ] { x y }$ 
C)  $6 \sqrt [ 11 ] { x y } - 2 x \sqrt [ 11 ] { x y }$ 
D)  Cannot simplify 
A)  $x \sqrt [ 11 ] { x y }$ 
B)  $2 x \sqrt [ 11 ] { x y }$ 
C)  $6 \sqrt [ 11 ] { x y } - 2 x \sqrt [ 11 ] { x y }$ 
D)  Cannot simplify

Question 5

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$$\frac { 2 + 2 i } { 7 - 6 i }$$

Accepted Answer

A)  $2 - 2 \mathrm { i }$ 
B)  $\frac { 26 } { 85 } + \frac { 2 } { 85 } \mathrm { i }$ 
C)  $\frac { 2 } { 85 } + \frac { 26 } { 85 } \mathrm { i }$ 
D)  $\frac { 2 } { 13 } - 2 i$ 
A)  $2 - 2 \mathrm { i }$ 
B)  $\frac { 26 } { 85 } + \frac { 2 } { 85 } \mathrm { i }$ 
C)  $\frac { 2 } { 85 } + \frac { 26 } { 85 } \mathrm { i }$ 
D)  $\frac { 2 } { 13 } - 2 i$

Question 6

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$\sqrt { 405 x ^ { 2 } }$$

Accepted Answer

A)  $405 x$ 
B)  $9 \sqrt { 5 x }$ 
C)  $9 x$ 
D)  $9 x \sqrt { 5 }$ 
A)  $405 x$ 
B)  $9 \sqrt { 5 x }$ 
C)  $9 x$ 
D)  $9 x \sqrt { 5 }$

Question 7

Solve the problem. Round the answer to the nearest hundredth.
-A pendulum has a length of 2.4 feet. Find its period. Use the formula $$\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }$$

Accepted Answer

A)  0.86 sec 
B)  2.15 sec 
C)  1.72 sec 
D)  1.22 sec 
A)  0.86 sec 
B)  2.15 sec 
C)  1.72 sec 
D)  1.22 sec

Question 8

Rationalize the denominator and simplify.
-$\frac { 5 } { 7 - \sqrt { 5 } }$

Accepted Answer

A)  $\frac { 35 + 5 \sqrt { 5 } } { - 2 }$ 
B)  $\frac { 35 + 5 \sqrt { 5 } } { 44 }$ 
C)  $\frac { 35 - 5 \sqrt { 5 } } { 44 }$ 
D)  $\frac { 5 } { 7 } - \frac { 5 } { \sqrt { 5 } }$ 
A)  $\frac { 35 + 5 \sqrt { 5 } } { - 2 }$ 
B)  $\frac { 35 + 5 \sqrt { 5 } } { 44 }$ 
C)  $\frac { 35 - 5 \sqrt { 5 } } { 44 }$ 
D)  $\frac { 5 } { 7 } - \frac { 5 } { \sqrt { 5 } }$

Question 9

Solve. Check for extraneous solutions.
-$( x - 6 ) ^ { 1 / 2 } = - 2$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 16 \}$ 
D)  $ \varnothing $ 
A)  $\{ 4 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 16 \}$ 
D)  $ \varnothing $

Question 10

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { - 343 }$$

Accepted Answer

A)  7 
B)  19 
C)  49 
D)  -7 
A)  7 
B)  19 
C)  49 
D)  -7

Question 11

Write the word or phrase that best completes each statement or answers the question.
-Choose values for n, a, and b to demonstrate the truth or falsity of the statement: $\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }$

Accepted Answer

The statem

Question 12

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }$$

Accepted Answer

A)  $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
D)  $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
A)  $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
D)  $x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y }$

Question 13

Add or subtract. Assume all variables represent nonnegative real numbers.
-$10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Accepted Answer

A)  $6 x \sqrt [ 4 ] { x ^ { 7 } }$ 
B)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
C)  $6 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $14 \sqrt [ 4 ] { x ^ { 3 } }$ 
A)  $6 x \sqrt [ 4 ] { x ^ { 7 } }$ 
B)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
C)  $6 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $14 \sqrt [ 4 ] { x ^ { 3 } }$

Question 14

Multiply. Write your answer in a + bi form.
-$$( 8 + 3 i ) ( 3 + 3 i )$$

Accepted Answer

A)  $33 - 15 \mathrm { i }$ 
B)  $15 - 33 \mathrm { i }$ 
C)  $15 + 33 \mathrm { i }$ 
D)  $9 i ^ { 2 } + 33 i + 24$ 
A)  $33 - 15 \mathrm { i }$ 
B)  $15 - 33 \mathrm { i }$ 
C)  $15 + 33 \mathrm { i }$ 
D)  $9 i ^ { 2 } + 33 i + 24$

Question 15

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

Accepted Answer

A)  $49 + 14 \sqrt { 7 }$ 
B)  $14 + 14 \sqrt { 7 }$ 
C)  $56 + 7 \sqrt { 7 }$ 
D)  $56 + 14 \sqrt { 7 }$ 
A)  $49 + 14 \sqrt { 7 }$ 
B)  $14 + 14 \sqrt { 7 }$ 
C)  $56 + 7 \sqrt { 7 }$ 
D)  $56 + 14 \sqrt { 7 }$

Question 16

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }$$

Accepted Answer

A)  $x y \sqrt { y ^ { 4 } z ^ { 3 } }$ 
B)  $x y z \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$ 
C)  $x y \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$ 
D)  $x \sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 3 } }$ 
A)  $x y \sqrt { y ^ { 4 } z ^ { 3 } }$ 
B)  $x y z \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$ 
C)  $x y \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }$ 
D)  $x \sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 3 } }$

Question 17

Multiply.
--4i ∙ 5i

Accepted Answer

A)  9 
B)  20 
C)  -9
D) -20 
A)  9 
B)  20 
C)  -9
D) -20

Question 18

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }$

Accepted Answer

A)  $\frac { 3 x } { y 2 } \sqrt { \frac { 5 x } { y } }$ 
B)  $\frac { x \sqrt { 45 x y } } { y 3 }$ 
C)  $\frac { 3 x \sqrt { 5 x y } } { y 3 }$ 
D)  $\frac { 3 x ^ { 3 } \sqrt { 5 } } { y 5 }$ 
A)  $\frac { 3 x } { y 2 } \sqrt { \frac { 5 x } { y } }$ 
B)  $\frac { x \sqrt { 45 x y } } { y 3 }$ 
C)  $\frac { 3 x \sqrt { 5 x y } } { y 3 }$ 
D)  $\frac { 3 x ^ { 3 } \sqrt { 5 } } { y 5 }$

Question 19

Simplify.
-i 10

Accepted Answer

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

Question 20

Solve the problem.
-The radius of a sphere depends on its surface area, S, and is given by the formula $$r = \sqrt { \frac { S } { 4 \pi } }$$

Accepted Answer

A)  98.5 square inches 
B)  17.6 square inches 
C)  393.9 square inches 
D)  70.3 square inches 
A)  98.5 square inches 
B)  17.6 square inches 
C)  393.9 square inches 
D)  70.3 square inches

Find the missing complex number. -(4 - 2i) + ? = 7 + 3i

Solve the problem. -For the function $f ( x ) = \sqrt [ 3 ] { 6 x + 6 } + 4$ , find all values $x$ for which $f ( x ) = 8$

Rationalize the denominator and simplify. - $\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $6 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 2 + 2 i } { 7 - 6 i }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt { 405 x ^ { 2 } }$

Solve the problem. Round the answer to the nearest hundredth. -A pendulum has a length of 2.4 feet. Find its period. Use the formula $\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }$

Rationalize the denominator and simplify. - $\frac { 5 } { 7 - \sqrt { 5 } }$

Solve. Check for extraneous solutions. - $( x - 6 ) ^ { 1 / 2 } = - 2$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { - 343 }$

Write the word or phrase that best completes each statement or answers the question. -Choose values for n, a, and b to demonstrate the truth or falsity of the statement: $\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Multiply. Write your answer in a + bi form. - $( 8 + 3 i ) ( 3 + 3 i )$

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }$

Multiply. --4i ∙ 5i

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }$

Simplify. -i¹⁰

Solve the problem. -The radius of a sphere depends on its surface area, S, and is given by the formula $r = \sqrt { \frac { S } { 4 \pi } }$

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

Find the missing complex number. -(4 - 2i) + ? = 7 + 3i

Solve the problem. -For the function f(x)=6x+63+4f ( x ) = \sqrt [ 3 ] { 6 x + 6 } + 4f(x)=36x+6​+4 , find all values xxx for which f(x)=8f ( x ) = 8f(x)=8

Rationalize the denominator and simplify. - 23+137107−33\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }107​−33​23​+137​​

Add or subtract. Assume all variables represent nonnegative real numbers. - 6x12y11−5xxy116 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }611x12y​−5x11xy​

Simplify by rationalizing the denominator. Write your answer in a +bi form. - 2+2i7−6i\frac { 2 + 2 i } { 7 - 6 i }7−6i2+2i​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 405x2\sqrt { 405 x ^ { 2 } }405x2​

Solve the problem. Round the answer to the nearest hundredth. -A pendulum has a length of 2.4 feet. Find its period. Use the formula T=2πL32\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }T=2π32L​​

Rationalize the denominator and simplify. - 57−5\frac { 5 } { 7 - \sqrt { 5 } }7−5​5​

Solve. Check for extraneous solutions. - (x−6)1/2=−2( x - 6 ) ^ { 1 / 2 } = - 2(x−6)1/2=−2

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −3433\sqrt [ 3 ] { - 343 }3−343​

Write the word or phrase that best completes each statement or answers the question. -Choose values for n, a, and b to demonstrate the truth or falsity of the statement: an+bn=a+bn\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }na​+nb​=na+b​

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - xy53⋅x19y143\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }3xy5​⋅3x19y14​

Add or subtract. Assume all variables represent nonnegative real numbers. - 10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7​−4x4x3​

Multiply. Write your answer in a + bi form. - (8+3i)(3+3i)( 8 + 3 i ) ( 3 + 3 i )(8+3i)(3+3i)

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - x6y10z36\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }6x6y10z3​