Question 1

Factor the given factor from the expression.
-$m ^ { - 1 / 2 } ; 8 m ^ { 9 / 4 } - 3 m ^ { - 1 / 2 }$

Accepted Answer

A)  $m ^ { - 1 / 2 } \left( 24 m ^ { 11 / 4 } - 8 \right)$ 
B)  $3 \mathrm {~m} ^ { - 1 / 4 } \left( 8 \mathrm {~m} ^ { 11 / 4 } - 1 \right)$ 
C)  $\mathrm { m } ^ { - 1 / 2 } \left( 8 \mathrm {~m} ^ { 9 / 4 } + 3 \right)$ 
D)  $\mathrm { m } ^ { - 1 / 2 } \left( 8 \mathrm {~m} ^ { 11 / 4 } - 3 \right)$ 
A)  $m ^ { - 1 / 2 } \left( 24 m ^ { 11 / 4 } - 8 \right)$ 
B)  $3 \mathrm {~m} ^ { - 1 / 4 } \left( 8 \mathrm {~m} ^ { 11 / 4 } - 1 \right)$ 
C)  $\mathrm { m } ^ { - 1 / 2 } \left( 8 \mathrm {~m} ^ { 9 / 4 } + 3 \right)$ 
D)  $\mathrm { m } ^ { - 1 / 2 } \left( 8 \mathrm {~m} ^ { 11 / 4 } - 3 \right)$

Question 2

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 7 } + 5 ) ( \sqrt { 7 } - 5 )$

Accepted Answer

A)  $- 18$ 
B)  2 
C)  $7 - 2 \sqrt { 5 }$ 
D)  32 
A)  $- 18$ 
B)  2 
C)  $7 - 2 \sqrt { 5 }$ 
D)  32

Question 3

Simplify. Assume that all variables represent any real number.
-$\sqrt { ( x + 8 ) ^ { 2 } }$

Accepted Answer

A)  $- x - 8$ 
B)  $x + 8$ 
C)  $- | x + 8 |$ 
D)  $| x + 8 |$ 
A)  $- x - 8$ 
B)  $x + 8$ 
C)  $- | x + 8 |$ 
D)  $| x + 8 |$

Question 4

Evaluate.
-If $f ( x ) = \sqrt [ 3 ] { x - 20 }$, find the value of $f ( 1 )$

Accepted Answer

A)  19 
B)  $\sqrt [ 3 ] { 19 }$ 
C)  $\sqrt [ 3 ] { - 19 }$ 
D)  $- 19$ 
A)  19 
B)  $\sqrt [ 3 ] { 19 }$ 
C)  $\sqrt [ 3 ] { - 19 }$ 
D)  $- 19$

Question 5

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

Accepted Answer

A)  15 + i 
B)  15 + 0i 
C)  -15 + 0i 
D)  15 + 12i 
A)  15 + i 
B)  15 + 0i 
C)  -15 + 0i 
D)  15 + 12i

Question 6

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 3 } \cdot \sqrt [ 3 ] { 9 }$

Accepted Answer

A)  27 
B)  $3 \sqrt [ 3 ] { 3 }$ 
C)  3 
D)  9 
A)  27 
B)  $3 \sqrt [ 3 ] { 3 }$ 
C)  3 
D)  9

Question 7

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 4 x - 3 } - 4 ) ^ { 2 }$

Accepted Answer

A)  $4 x - 8 \sqrt { 4 x - 3 } + 13$ 
B)  $4 x - 8 \sqrt { 4 x - 3 } + 16$ 
C)  $4 x + 16 \sqrt { 4 x - 3 } + 16$ 
D)  $4 x + 16 \sqrt { 4 x - 3 } + 13$ 
A)  $4 x - 8 \sqrt { 4 x - 3 } + 13$ 
B)  $4 x - 8 \sqrt { 4 x - 3 } + 16$ 
C)  $4 x + 16 \sqrt { 4 x - 3 } + 16$ 
D)  $4 x + 16 \sqrt { 4 x - 3 } + 13$

Question 8

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

Accepted Answer

A)  3 - 2i 
B)  -3 + 4i 
C)  -3 + 2i 
D)  3 - 4i 
A)  3 - 2i 
B)  -3 + 4i 
C)  -3 + 2i 
D)  3 - 4i

Question 9

Solve.
-A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 60 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 80 feet long.

Accepted Answer

A)  $2 \sqrt { 70 } \mathrm { ft }$ 
B)  $2 \sqrt { 5 } \mathrm { ft }$ 
C)  $20 \sqrt { 7 } \mathrm { ft }$ 
D)  $100 \mathrm { ft }$ 
A)  $2 \sqrt { 70 } \mathrm { ft }$ 
B)  $2 \sqrt { 5 } \mathrm { ft }$ 
C)  $20 \sqrt { 7 } \mathrm { ft }$ 
D)  $100 \mathrm { ft }$

Question 10

Solve.
-$\sqrt { x } - 2 = \sqrt { x + 32 }$

Accepted Answer

A)  $- 49$ 
B)  $\varnothing$ 
C)  $- 7$ 
D)  49 
A)  $- 49$ 
B)  $\varnothing$ 
C)  $- 7$ 
D)  49

Question 11

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { index rationalizing } & \text { conjugate } & \text { principal square rootcube root midpoint } \
\text { complex numberlike radicals } & \text { radicand } & \text { imaginary unit } \quad \text { distance }
\end{array}$$
-The_________ of a number is written as $\sqrt [ 3 ] { \mathrm { a } }$.

Accepted Answer

A)  midpoint 
B)  cube root 
C)  distance 
D)  principal square root 
A)  midpoint 
B)  cube root 
C)  distance 
D)  principal square root

Question 12

Solve.
-$\sqrt { 3 x + 2 } - 5 = 0$

Accepted Answer

A)  $\frac { 23 } { 3 }$ 
B)  $\frac { 3 } { 23 }$ 
C)  $\varnothing$ 
D)  69 
A)  $\frac { 23 } { 3 }$ 
B)  $\frac { 3 } { 23 }$ 
C)  $\varnothing$ 
D)  69

Question 13

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 81 n ^ { 4 } }$

Accepted Answer

A)  $- 6 n$ 
B)  $6 n$ 
C)  $- 1 \mathrm { n }$ 
D)  $5 \mathrm { n }$ 
A)  $- 6 n$ 
B)  $6 n$ 
C)  $- 1 \mathrm { n }$ 
D)  $5 \mathrm { n }$

Question 14

Simplify. Assume that all variables represent any real number.
-$\sqrt { ( - 7 ) ^ { 2 } }$

Accepted Answer

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

Question 15

Find the root. Assume that all variables represent nonnegative real numbers.
-$\sqrt [ 6 ] { x ^ { 48 } }$

Accepted Answer

A)  $x ^ { 9 }$ 
B)  $8 x$ 
C)  $x ^ { 8 }$ 
D)  $x ^ { 6 }$ 
A)  $x ^ { 9 }$ 
B)  $8 x$ 
C)  $x ^ { 8 }$ 
D)  $x ^ { 6 }$

Question 16

Perform the indicated operation. Write the result in the form a + bi.
-(6i)(15i)

Accepted Answer

A)  90 + 0i 
B)  -90 + 0i 
C)  0 - 90i 
D)  0 + 90i 
A)  90 + 0i 
B)  -90 + 0i 
C)  0 - 90i 
D)  0 + 90i

Question 17

Perform the indicated operation. Write the result in the form a + bi.
-(24 - 3i)(8 + i)

Accepted Answer

A)  189 + 0i 
B)  195 + 0i 
C)  195 - 48i 
D)  195 - 24i 
A)  189 + 0i 
B)  195 + 0i 
C)  195 - 48i 
D)  195 - 24i

Question 18

Solve.
-$\sqrt { 30 x - 15 } = x + 7$

Accepted Answer

A)  $- 8$ 
B)  8 
C)  $- 7$ 
D)  6 
A)  $- 8$ 
B)  8 
C)  $- 7$ 
D)  6

Question 19

Write in terms of i.
-$\sqrt { - 245 }$

Accepted Answer

A)  $- 7 i \sqrt { 5 }$ 
B)  $- 7 \sqrt { 5 }$ 
C)  $7 \sqrt { 5 }$ 
D)  $7 \mathrm { i } \sqrt { 5 }$ 
A)  $- 7 i \sqrt { 5 }$ 
B)  $- 7 \sqrt { 5 }$ 
C)  $7 \sqrt { 5 }$ 
D)  $7 \mathrm { i } \sqrt { 5 }$

Factor the given factor from the expression. - $m ^ { - 1 / 2 } ; 8 m ^ { 9 / 4 } - 3 m ^ { - 1 / 2 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 7 } + 5 ) ( \sqrt { 7 } - 5 )$

Simplify. Assume that all variables represent any real number. - $\sqrt { ( x + 8 ) ^ { 2 } }$

Evaluate. -If $f ( x ) = \sqrt [ 3 ] { x - 20 }$ , find the value of $f ( 1 )$

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

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 3 } \cdot \sqrt [ 3 ] { 9 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 4 x - 3 } - 4 ) ^ { 2 }$

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

Solve. -A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 60 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 80 feet long.

Solve. - $\sqrt { x } - 2 = \sqrt { x + 32 }$

Fill in the blank with one of the words or phrases listed below. index rationalizing conjugate principal square rootcube root midpoint complex numberlike radicals radicand imaginary unit distance -The_________ of a number is written as $\sqrt [ 3 ] { \mathrm { a } }$ .

Solve. - $\sqrt { 3 x + 2 } - 5 = 0$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 81 n ^ { 4 } }$

Simplify. Assume that all variables represent any real number. - $\sqrt { ( - 7 ) ^ { 2 } }$

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 6 ] { x ^ { 48 } }$

Perform the indicated operation. Write the result in the form a + bi. -(6i)(15i)

Perform the indicated operation. Write the result in the form a + bi. -(24 - 3i)(8 + i)

Solve. - $\sqrt { 30 x - 15 } = x + 7$

Write in terms of i. - $\sqrt { - 245 }$

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

Factor the given factor from the expression. - m−1/2;8m9/4−3m−1/2m ^ { - 1 / 2 } ; 8 m ^ { 9 / 4 } - 3 m ^ { - 1 / 2 }m−1/2;8m9/4−3m−1/2

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (7+5)(7−5)( \sqrt { 7 } + 5 ) ( \sqrt { 7 } - 5 )(7​+5)(7​−5)

Simplify. Assume that all variables represent any real number. - (x+8)2\sqrt { ( x + 8 ) ^ { 2 } }(x+8)2​

Evaluate. -If f(x)=x−203f ( x ) = \sqrt [ 3 ] { x - 20 }f(x)=3x−20​ , find the value of f(1)f ( 1 )f(1)