Question 1

Perform the indicated operation. Write the result in the form a + bi.
-(-4i)(-7i)

Accepted Answer

A)  28 + 0i 
B)  0 + 28i 
C)  -28 + 0i 
D)  0 - 28i 
A)  28 + 0i 
B)  0 + 28i 
C)  -28 + 0i 
D)  0 - 28i

Question 2

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { 8 - \sqrt { 10 } } { 7 }$

Accepted Answer

A)  $\frac { 8 } { 7 } - \frac { \sqrt { 10 } } { 7 }$ 
B)  $\frac { 2 } { 56 + 7 \sqrt { 10 } }$ 
C)  $\frac { 54 } { 56 - 7 \sqrt { 10 } }$ 
D)  $\frac { 54 } { 56 + 7 \sqrt { 10 } }$ 
A)  $\frac { 8 } { 7 } - \frac { \sqrt { 10 } } { 7 }$ 
B)  $\frac { 2 } { 56 + 7 \sqrt { 10 } }$ 
C)  $\frac { 54 } { 56 - 7 \sqrt { 10 } }$ 
D)  $\frac { 54 } { 56 + 7 \sqrt { 10 } }$

Question 3

Solve the problem.
-Find x.

Accepted Answer

A)  15 
B)  $\frac { 15 \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 30 } } { 2 }$ 
D)  $15 \sqrt { 2 }$ 
A)  15 
B)  $\frac { 15 \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 30 } } { 2 }$ 
D)  $15 \sqrt { 2 }$

Question 4

Simplify. Assume that all variables represent any real number.
-$\sqrt [ 5 ] { ( - 11 ) ^ { 5 } }$

Accepted Answer

A)  55 
B)  11 
C)  $- 55$ 
D)  $- 11$ 
A)  55 
B)  11 
C)  $- 55$ 
D)  $- 11$

Question 5

Perform the indicated operation. Write the result in the form a + bi.
-(14i)(-7i)

Accepted Answer

A)  98 + 0i 
B)  0 + 98i 
C)  0 - 98i 
D)  -98 + 0i 
A)  98 + 0i 
B)  0 + 98i 
C)  0 - 98i 
D)  -98 + 0i

Question 6

Use the quotient rule to divide and simplify.
-$\frac { \sqrt { 18 } } { \sqrt { 900 } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 2 } } { 30 }$ 
B)  $\sqrt { \frac { 18 } { 900 } }$ 
C)  $\frac { \sqrt { 2 } } { 10 }$ 
D)  $\sqrt { \frac { 2 } { 100 } }$ 
A)  $\frac { 3 \sqrt { 2 } } { 30 }$ 
B)  $\sqrt { \frac { 18 } { 900 } }$ 
C)  $\frac { \sqrt { 2 } } { 10 }$ 
D)  $\sqrt { \frac { 2 } { 100 } }$

Question 7

Find the root. Use absolute value bars when necessary.
-$\sqrt [ 7 ] { ( - 7 ) ^ { 7 } }$

Accepted Answer

A)  7 
B)  $( - 7 ) ^ { 7 }$ 
C)  $- 7$ 
D)  $| - 7 |$ 
A)  7 
B)  $( - 7 ) ^ { 7 }$ 
C)  $- 7$ 
D)  $| - 7 |$

Question 8

Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\frac { \left( 2 x ^ { 1 / 4 } \right) ^ { 7 } } { x ^ { - 2 / 7 } }$

Accepted Answer

A)  $128 x ^ { 41 / 28 }$ 
B)  $128 x ^ { 57 / 28 }$ 
C)  $2 x ^ { 41 / 28 }$ 
D)  $2 x ^ { 57 / 28 }$ 
A)  $128 x ^ { 41 / 28 }$ 
B)  $128 x ^ { 57 / 28 }$ 
C)  $2 x ^ { 41 / 28 }$ 
D)  $2 x ^ { 57 / 28 }$

Question 9

Solve.
-$\sqrt { 9 x - 2 } = \sqrt { 2 - 9 x }$

Accepted Answer

A)  $\frac { 9 } { 2 }$ 
B)  $\frac { 2 } { 9 }$ 
C)  $\varnothing$ 
D)  $- \frac { 2 } { 9 }$ 
A)  $\frac { 9 } { 2 }$ 
B)  $\frac { 2 } { 9 }$ 
C)  $\varnothing$ 
D)  $- \frac { 2 } { 9 }$

Question 10

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 6 } { 36 } } + \sqrt { \frac { 384 } { 25 } }$

Accepted Answer

A)  $\frac { 53 \sqrt { 6 } } { 30 }$ 
B)  $\frac { 53 \sqrt { 6 } } { 6 }$ 
C)  $\frac { - 43 \sqrt { 6 } } { 30 }$ 
D)  $\frac { 6 \sqrt { 53 } } { 30 }$ 
A)  $\frac { 53 \sqrt { 6 } } { 30 }$ 
B)  $\frac { 53 \sqrt { 6 } } { 6 }$ 
C)  $\frac { - 43 \sqrt { 6 } } { 30 }$ 
D)  $\frac { 6 \sqrt { 53 } } { 30 }$

Question 11

Perform the indicated operation and simplify. Write the result in the form a $a + bi$
-$- \sqrt { - 268 }$

Accepted Answer

A)  $2 \sqrt { 67 } + 0 \mathrm { i }$ 
B)  $0 + 2 i \sqrt { 67 }$ 
C)  $0 - 2 i \sqrt { 67 }$ 
D)  $- 2 \sqrt { 67 } + 0 \mathrm { i }$ 
A)  $2 \sqrt { 67 } + 0 \mathrm { i }$ 
B)  $0 + 2 i \sqrt { 67 }$ 
C)  $0 - 2 i \sqrt { 67 }$ 
D)  $- 2 \sqrt { 67 } + 0 \mathrm { i }$

Question 12

Use radical notation to write the expression. Simplify if possible.
-$121 ^ { 1 / 2 }$

Accepted Answer

A)  11 
B)  44 
C)  $5.5$ 
D)  22 
A)  11 
B)  44 
C)  $5.5$ 
D)  22

Question 13

Find the root. Assume that all variables represent nonnegative real numbers.
-$\sqrt [ 4 ] { - 16 }$

Accepted Answer

A)  4 
B)  not a real number 
C)  2 
D)  $- 2$ 
A)  4 
B)  not a real number 
C)  2 
D)  $- 2$

Question 14

Solve.
-$- \sqrt { 5 x + 1 } = - 8$

Accepted Answer

A)  $\frac { 5 } { 63 }$ 
B)  $\varnothing$ 
C)  $\frac { 63 } { 5 }$ 
D)  315 
A)  $\frac { 5 } { 63 }$ 
B)  $\varnothing$ 
C)  $\frac { 63 } { 5 }$ 
D)  315

Question 15

Perform the indicated operation and simplify. Write the result in the form a $a + bi$
-$( 3 - 4 i ) - ( 3 - i )$

Accepted Answer

A)  $0 - 3 \mathrm { i }$ 
B)  $6 - 5 i$ 
C)  $6 - 3 i$ 
D)  $0 - 5 i$ 
A)  $0 - 3 \mathrm { i }$ 
B)  $6 - 5 i$ 
C)  $6 - 3 i$ 
D)  $0 - 5 i$

Question 16

Solve.
-$\sqrt { 1 + 8 \sqrt { x } } = 1 + \sqrt { x }$

Accepted Answer

A)  0,100 
B)  0,36 
C)  $0 , \frac { 4 } { 7 }$ 
D)  0,64 
A)  0,100 
B)  0,36 
C)  $0 , \frac { 4 } { 7 }$ 
D)  0,64

Question 17

Perform the indicated operation. Write the result in the form a + bi.
-(8 - 7i) + (6 + 9i)

Accepted Answer

A)  14 - 2i 
B)  -14 - 2i 
C)  14 + 2i 
D)  2 + 16i 
A)  14 - 2i 
B)  -14 - 2i 
C)  14 + 2i 
D)  2 + 16i

Question 18

Find the distance between the pair of points.
-$( 3.2,4.3 )$ and $( - 6.9 , - 5.8 )$
Approximate the distance to two decimal places.

Accepted Answer

A)  $3.99$ units 
B)  $10.21$ units 
C)  $14.28$ units 
D)  $10.76$ units 
A)  $3.99$ units 
B)  $10.21$ units 
C)  $14.28$ units 
D)  $10.76$ units

Question 19

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  $\sqrt { 71 }$ 
B)  $\sqrt { 57 }$ 
C)  57 
D)  $\sqrt { 15 }$ 
A)  $\sqrt { 71 }$ 
B)  $\sqrt { 57 }$ 
C)  57 
D)  $\sqrt { 15 }$

Question 20

Solve.
-The number of centimeters, $d$, that a spring is compressed from its natural, uncompressed position is given by the formula $d = \sqrt { \frac { 2 W } { k } }$, where $W$ is the number of joules of work done to move the spring and $\mathrm { k }$ is the spring constant. If a spring has a spring constant of $0.2$, find the amount of work needed to move the spring 7 centimeters.

Accepted Answer

A)  $4.9$ joules 
B)  49 joules 
C)  $9.8$ joules 
D)  $0.7$ joules 
A)  $4.9$ joules 
B)  49 joules 
C)  $9.8$ joules 
D)  $0.7$ joules

Perform the indicated operation. Write the result in the form a + bi. -(-4i)(-7i)

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { 8 - \sqrt { 10 } } { 7 }$

Solve the problem. -Find x.

Simplify. Assume that all variables represent any real number. - $\sqrt [ 5 ] { ( - 11 ) ^ { 5 } }$

Perform the indicated operation. Write the result in the form a + bi. -(14i)(-7i)

Use the quotient rule to divide and simplify. - $\frac { \sqrt { 18 } } { \sqrt { 900 } }$

Find the root. Use absolute value bars when necessary. - $\sqrt [ 7 ] { ( - 7 ) ^ { 7 } }$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\frac { \left( 2 x ^ { 1 / 4 } \right) ^ { 7 } } { x ^ { - 2 / 7 } }$

Solve. - $\sqrt { 9 x - 2 } = \sqrt { 2 - 9 x }$

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { \frac { 6 } { 36 } } + \sqrt { \frac { 384 } { 25 } }$

Perform the indicated operation and simplify. Write the result in the form a $a + bi$ - $- \sqrt { - 268 }$

Use radical notation to write the expression. Simplify if possible. - $121 ^ { 1 / 2 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 4 ] { - 16 }$

Solve. - $- \sqrt { 5 x + 1 } = - 8$

Perform the indicated operation and simplify. Write the result in the form a $a + bi$ - $( 3 - 4 i ) - ( 3 - i )$

Solve. - $\sqrt { 1 + 8 \sqrt { x } } = 1 + \sqrt { x }$

Perform the indicated operation. Write the result in the form a + bi. -(8 - 7i) + (6 + 9i)

Find the distance between the pair of points. - $( 3.2,4.3 )$ and $( - 6.9 , - 5.8 )$ Approximate the distance to two decimal places.

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers