Question 1

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 2 + 3 i } { 5 + 2 i }$

Accepted Answer

A)  $\frac { 4 } { 29 } - \frac { 19 } { 29 } \mathrm { i }$ 
B)  $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$ 
C)  $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
D)  $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
A)  $\frac { 4 } { 29 } - \frac { 19 } { 29 } \mathrm { i }$ 
B)  $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$ 
C)  $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$ 
D)  $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

Question 2

Approximate to the nearest thousandth, using a calculator.
-$\sqrt { 3 }$

Accepted Answer

A)  $1.737$ 
B)  $3.000$ 
C)  $1.732$ 
D)  $1.729$ 
A)  $1.737$ 
B)  $3.000$ 
C)  $1.732$ 
D)  $1.729$

Question 3

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\frac { 9 } { \sqrt { 22 } }$

Accepted Answer

A)  $\frac { 81 \sqrt { 22 } } { 22 }$ 
B)  493 
C)  $9 \sqrt { 22 }$ 
D)  $\frac { 9 \sqrt { 22 } } { 22 }$ 
A)  $\frac { 81 \sqrt { 22 } } { 22 }$ 
B)  493 
C)  $9 \sqrt { 22 }$ 
D)  $\frac { 9 \sqrt { 22 } } { 22 }$

Question 4

Simplify. Assume all variables represent nonnegative values.
-$\frac { \sqrt { 4 x y ^ { 3 } } } { \sqrt { 2 x } }$

Accepted Answer

A)  $y ^ { 2 } \sqrt { 2 x y }$ 
B)  $y ^ { 2 } \sqrt { 4 y }$ 
C)  $\mathrm { y } \sqrt { 2 \mathrm { y } }$ 
D)  $y ^ { 2 } \sqrt { 2 y }$ 
A)  $y ^ { 2 } \sqrt { 2 x y }$ 
B)  $y ^ { 2 } \sqrt { 4 y }$ 
C)  $\mathrm { y } \sqrt { 2 \mathrm { y } }$ 
D)  $y ^ { 2 } \sqrt { 2 y }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$- \sqrt [ 4 ] { 1024 }$

Accepted Answer

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

Question 6

Approximate to the nearest thousandth, using a calculator.
-$$\sqrt { 0.000193 }$$

Accepted Answer

A)  0.140 
B)  1.400 
C)  0.001 
D)  0.014 
A)  0.140 
B)  1.400 
C)  0.001 
D)  0.014

Question 7

Divide.
-$$( 4 + 2 i ) \div ( 6 + 7 i )$$

Accepted Answer

A)  $- \frac { 10 } { 13 } - \frac { 16 } { 13 }$ i 
B)  $\frac { 38 } { 85 } - \frac { 16 } { 85 } \mathrm { i }$ 
C)  $\frac { 2 } { 17 } - \frac { 8 } { 17 } \mathrm { i }$ 
D)  $- \frac { 38 } { 13 } - \frac { 16 } { 13 } \mathrm { i }$ 
A)  $- \frac { 10 } { 13 } - \frac { 16 } { 13 }$ i 
B)  $\frac { 38 } { 85 } - \frac { 16 } { 85 } \mathrm { i }$ 
C)  $\frac { 2 } { 17 } - \frac { 8 } { 17 } \mathrm { i }$ 
D)  $- \frac { 38 } { 13 } - \frac { 16 } { 13 } \mathrm { i }$

Question 8

Multiply. Write your answer in a + bi form.
-$7 \mathrm { i } ( 8 - 8 \mathrm { i } )$

Accepted Answer

A)  $56 i + 56 i ^ { 2 }$ 
B)  $56 + 56 \mathrm { i }$ 
C)  $56 \mathrm { i } - 56 \mathrm { i } ^ { 2 }$ 
D)  $56 \mathrm { i } - 56$ 
A)  $56 i + 56 i ^ { 2 }$ 
B)  $56 + 56 \mathrm { i }$ 
C)  $56 \mathrm { i } - 56 \mathrm { i } ^ { 2 }$ 
D)  $56 \mathrm { i } - 56$

Question 9

Add or subtract.
-$$12 \sqrt [ 3 ] { 3 } + 4 \sqrt [ 3 ] { 3 }$$

Accepted Answer

A)  $16 \sqrt [ 3 ] { 9 }$ 
B)  $- 8 \sqrt [ 3 ] { 3 }$ 
C)  $16 \sqrt [ 3 ] { 6 }$ 
D)  $16 \sqrt [ 3 ] { 3 }$ 
A)  $16 \sqrt [ 3 ] { 9 }$ 
B)  $- 8 \sqrt [ 3 ] { 3 }$ 
C)  $16 \sqrt [ 3 ] { 6 }$ 
D)  $16 \sqrt [ 3 ] { 3 }$

Question 10

Find the missing complex number.
-$$( 7 - 9 \mathrm { i } ) ( ? ) = 9 + 2 \mathrm { i }$$

Accepted Answer

A)  $\frac { 81 } { 26 } + \frac { 67 } { 26 } \mathrm { i }$ 
B)  $- \frac { 9 } { 32 } + \frac { 19 } { 32 } \mathrm { i }$ 
C)  $- \frac { 81 } { 32 } + \frac { 19 } { 32 } \mathrm { i }$ 
D)  $\frac { 9 } { 26 } + \frac { 19 } { 26 } \mathrm { i }$ 
A)  $\frac { 81 } { 26 } + \frac { 67 } { 26 } \mathrm { i }$ 
B)  $- \frac { 9 } { 32 } + \frac { 19 } { 32 } \mathrm { i }$ 
C)  $- \frac { 81 } { 32 } + \frac { 19 } { 32 } \mathrm { i }$ 
D)  $\frac { 9 } { 26 } + \frac { 19 } { 26 } \mathrm { i }$

Question 11

Add or subtract.
-$5 \sqrt { 3 } + 8 \sqrt { 3 }$

Accepted Answer

A)  42 
B)  $14 \sqrt { 3 }$ 
C)  $48 \sqrt { 3 }$ 
D)  $14 \sqrt { 6 }$ 
A)  42 
B)  $14 \sqrt { 3 }$ 
C)  $48 \sqrt { 3 }$ 
D)  $14 \sqrt { 6 }$

Question 12

Approximate to the nearest thousandth, using a calculator.
-$$- \sqrt { 13 }$$

Accepted Answer

A)  -13.000 
B)  -3.603 
C)  -3.606 
D)  -3.611 
A)  -13.000 
B)  -3.603 
C)  -3.606 
D)  -3.611

Question 13

Evaluate the radical function at the given value of the variable.
-$$f ( x ) = \sqrt [ 4 ] { x - 20 }$$

Accepted Answer

A)  $[ 20 , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 20 , \infty )$ 
A)  $[ 20 , \infty )$ 
B)  $[ 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $[ - 20 , \infty )$

Question 14

Approximate to the nearest thousandth, using a calculator.
-$$\sqrt { 0.00181 }$$

Accepted Answer

A)  0.004 
B)  4.300 
C)  0.430 
D)  0.043 
A)  0.004 
B)  4.300 
C)  0.430 
D)  0.043

Question 15

Solve. Check for extraneous solutions.
-$$x ^ { 1 / 3 } - 2 = 4$$

Accepted Answer

A)  $\{ 64 \}$ 
B)  $\{ 36 \}$ 
C)  $\{ \sqrt [ 3 ] { 6 } \}$ 
D)  $\{ 216 \}$ 
A)  $\{ 64 \}$ 
B)  $\{ 36 \}$ 
C)  $\{ \sqrt [ 3 ] { 6 } \}$ 
D)  $\{ 216 \}$

Question 16

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { - 9 } { - 4 + 8 i }$

Accepted Answer

A)  $- \frac { 3 } { 4 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $\frac { 9 } { 20 } - \frac { 9 } { 10 } \mathrm { i }$ 
C)  $- \frac { 3 } { 4 } - \frac { 3 } { 2 } \mathrm { i }$ 
D)  $\frac { 9 } { 20 } + \frac { 9 } { 10 } \mathrm { i }$ 
A)  $- \frac { 3 } { 4 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $\frac { 9 } { 20 } - \frac { 9 } { 10 } \mathrm { i }$ 
C)  $- \frac { 3 } { 4 } - \frac { 3 } { 2 } \mathrm { i }$ 
D)  $\frac { 9 } { 20 } + \frac { 9 } { 10 } \mathrm { i }$

Question 17

Find the missing complex number.
-$$\frac { ? } { 7 + 9 i } = 8 + 9 i$$

Accepted Answer

A)  $137 + 9 i$ 
B)  $- 25 + 135 i$ 
C)  $- 25 - 135 \mathrm { i }$ 
D)  $81 i ^ { 2 } + 135 i + 56$ 
A)  $137 + 9 i$ 
B)  $- 25 + 135 i$ 
C)  $- 25 - 135 \mathrm { i }$ 
D)  $81 i ^ { 2 } + 135 i + 56$

Question 18

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt { t ^ { 11 } }$

Accepted Answer

A)  $t ^ { 11 } \sqrt { t }$ 
B)  $t \sqrt { t }$ 
C)  $t ^ { 22 } \sqrt { t }$ 
D)  $t 6 \sqrt { t }$ 
A)  $t ^ { 11 } \sqrt { t }$ 
B)  $t \sqrt { t }$ 
C)  $t ^ { 22 } \sqrt { t }$ 
D)  $t 6 \sqrt { t }$

Question 19

Solve the problem.
-The radius, r, of a right circular cone can be found using the formula $$\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } }$$

Accepted Answer

A)  10.8 in. 
B)  6.3 in. 
C)  11.3 in. 
D)  5.4 in. 
A)  10.8 in. 
B)  6.3 in. 
C)  11.3 in. 
D)  5.4 in.

Question 20

Multiply. Write your answer in a + bi form.
-$$( 3 - 4 \mathrm { i } ) ( 2 - 5 \mathrm { i } )$$

Accepted Answer

A)  $20 i ^ { 2 } - 23 i + 6$ 
B)  $26 + 7 \mathrm { i }$ 
C)  $- 14 + 23 \mathrm { i }$ 
D)  $- 14 - 23 \mathrm { i }$ 
A)  $20 i ^ { 2 } - 23 i + 6$ 
B)  $26 + 7 \mathrm { i }$ 
C)  $- 14 + 23 \mathrm { i }$ 
D)  $- 14 - 23 \mathrm { i }$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 2 + 3 i } { 5 + 2 i }$

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 3 }$

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\frac { 9 } { \sqrt { 22 } }$

Simplify. Assume all variables represent nonnegative values. - $\frac { \sqrt { 4 x y ^ { 3 } } } { \sqrt { 2 x } }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $- \sqrt [ 4 ] { 1024 }$

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 0.000193 }$

Divide. - $( 4 + 2 i ) \div ( 6 + 7 i )$

Multiply. Write your answer in a + bi form. - $7 \mathrm { i } ( 8 - 8 \mathrm { i } )$

Add or subtract. - $12 \sqrt [ 3 ] { 3 } + 4 \sqrt [ 3 ] { 3 }$

Find the missing complex number. - $( 7 - 9 \mathrm { i } ) ( ? ) = 9 + 2 \mathrm { i }$

Add or subtract. - $5 \sqrt { 3 } + 8 \sqrt { 3 }$

Approximate to the nearest thousandth, using a calculator. - $- \sqrt { 13 }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt [ 4 ] { x - 20 }$

Approximate to the nearest thousandth, using a calculator. - $\sqrt { 0.00181 }$

Solve. Check for extraneous solutions. - $x ^ { 1 / 3 } - 2 = 4$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { - 9 } { - 4 + 8 i }$

Find the missing complex number. - $\frac { ? } { 7 + 9 i } = 8 + 9 i$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt { t ^ { 11 } }$

Solve the problem. -The radius, r, of a right circular cone can be found using the formula $\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } }$

Multiply. Write your answer in a + bi form. - $( 3 - 4 \mathrm { i } ) ( 2 - 5 \mathrm { i } )$

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 by rationalizing the denominator. Write your answer in a +bi form. - 2+3i5+2i\frac { 2 + 3 i } { 5 + 2 i }5+2i2+3i​

Approximate to the nearest thousandth, using a calculator. - 3\sqrt { 3 }3​

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - 922\frac { 9 } { \sqrt { 22 } }22​9​

Simplify. Assume all variables represent nonnegative values. - 4xy32x\frac { \sqrt { 4 x y ^ { 3 } } } { \sqrt { 2 x } }2x​4xy3​​

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - −10244- \sqrt [ 4 ] { 1024 }−41024​

Approximate to the nearest thousandth, using a calculator. - 0.000193\sqrt { 0.000193 }0.000193​

Divide. - (4+2i)÷(6+7i)( 4 + 2 i ) \div ( 6 + 7 i )(4+2i)÷(6+7i)

Multiply. Write your answer in a + bi form. - 7i(8−8i)7 \mathrm { i } ( 8 - 8 \mathrm { i } )7i(8−8i)

Add or subtract. - 1233+43312 \sqrt [ 3 ] { 3 } + 4 \sqrt [ 3 ] { 3 }1233​+433​

Find the missing complex number. - (7−9i)(?)=9+2i( 7 - 9 \mathrm { i } ) ( ? ) = 9 + 2 \mathrm { i }(7−9i)(?)=9+2i

Add or subtract. - 53+835 \sqrt { 3 } + 8 \sqrt { 3 }53​+83​

Approximate to the nearest thousandth, using a calculator. - −13- \sqrt { 13 }−13​

Evaluate the radical function at the given value of the variable. - f(x)=x−204f ( x ) = \sqrt [ 4 ] { x - 20 }f(x)=4x−20​

Approximate to the nearest thousandth, using a calculator. - 0.00181\sqrt { 0.00181 }0.00181​

Solve. Check for extraneous solutions. - x1/3−2=4x ^ { 1 / 3 } - 2 = 4x1/3−2=4

Simplify by rationalizing the denominator. Write your answer in a +bi form. - −9−4+8i\frac { - 9 } { - 4 + 8 i }−4+8i−9​

Find the missing complex number. - ?7+9i=8+9i\frac { ? } { 7 + 9 i } = 8 + 9 i7+9i?​=8+9i

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - t11\sqrt { t ^ { 11 } }t11​

Solve the problem. -The radius, r, of a right circular cone can be found using the formula r=3 Vπh\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } }r=πh3 V​​

Multiply. Write your answer in a + bi form. - (3−4i)(2−5i)( 3 - 4 \mathrm { i } ) ( 2 - 5 \mathrm { i } )(3−4i)(2−5i)