Question 1

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

Accepted Answer

A)  19 
B)  $\frac { 361 } { 2 }$ 
C)  361 
D)  $\frac { 19 } { 2 }$ 
A)  19 
B)  $\frac { 361 } { 2 }$ 
C)  361 
D)  $\frac { 19 } { 2 }$

Question 2

Find the cube root.
-$\sqrt [ 3 ] { 216 }$

Accepted Answer

A)  36 
B)  not a real number 
C)  14 
D)  6 
A)  36 
B)  not a real number 
C)  14 
D)  6

Question 3

Use rational exponents to write as a single radical expression.
-$\sqrt [ 5 ] { 3 } \cdot \sqrt [ 3 ] { x }$

Accepted Answer

A)  $\sqrt [ 15 ] { 3 x }$ 
B)  $\sqrt [ 5 ] { 3 x }$ 
C)  $\sqrt [ 15 ] { 3 x ^ { 5 } }$ 
D)  $\sqrt [ 15 ] { 27 x ^ { 5 } }$ 
A)  $\sqrt [ 15 ] { 3 x }$ 
B)  $\sqrt [ 5 ] { 3 x }$ 
C)  $\sqrt [ 15 ] { 3 x ^ { 5 } }$ 
D)  $\sqrt [ 15 ] { 27 x ^ { 5 } }$

Question 4

Factor the given factor from the expression.
-$x ^ { 2 / 5 } ; x ^ { 4 / 5 } + 3 x ^ { 2 / 5 }$

Accepted Answer

A)  $x ^ { 1 / 5 } \left( x ^ { 4 / 5 } + 3 \right)$ 
B)  $x ^{1 / 5} \left( x ^ { 2 / 5 + 3 } \right)$ 
C)  $x ^ { 2 / 5 } \left( x ^ { 2 / 5 } + 3 \right)$ 
D)  $x ^ { 2 / 5 } \left( x ^ { - 2 / 5 } + 3 \right)$ 
A)  $x ^ { 1 / 5 } \left( x ^ { 4 / 5 } + 3 \right)$ 
B)  $x ^{1 / 5} \left( x ^ { 2 / 5 + 3 } \right)$ 
C)  $x ^ { 2 / 5 } \left( x ^ { 2 / 5 } + 3 \right)$ 
D)  $x ^ { 2 / 5 } \left( x ^ { - 2 / 5 } + 3 \right)$

Question 5

Solve.
-$\sqrt [ 3 ] { 10 x - 2 } = \sqrt [ 3 ] { x + 12 }$

Accepted Answer

A)  $\frac { 7 } { 5 }$ 
B)  $\frac { 10 } { 9 }$ 
C)  $\frac { 14 } { 9 }$ 
D)  $\frac { 10 } { 11 }$ 
A)  $\frac { 7 } { 5 }$ 
B)  $\frac { 10 } { 9 }$ 
C)  $\frac { 14 } { 9 }$ 
D)  $\frac { 10 } { 11 }$

Question 6

Identify the domain and then graph the function.
-$f ( x ) = \sqrt { x - 3 } ; \text { use the following table. }$

Accepted Answer

A)  $[ 0 , \infty )$
  
B)  $[ 0 , \infty )$
  
C)  $[ - 3 , \infty )$
  
D)  $[ 3 , \infty )$
  
A)  $[ 0 , \infty )$
  
B)  $[ 0 , \infty )$
  
C)  $[ - 3 , \infty )$
  
D)  $[ 3 , \infty )$

Question 7

Solve.
-$\sqrt [ 3 ] { x + 3 } = \sqrt [ 3 ] { 9 x - 2 }$

Accepted Answer

A)  $\frac { 5 } { 8 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 5 } { 9 }$ 
D)  $\frac { 1 } { 10 }$ 
A)  $\frac { 5 } { 8 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 5 } { 9 }$ 
D)  $\frac { 1 } { 10 }$

Question 8

Solve.
-$\sqrt [ 3 ] { 5 x } = - 2$

Accepted Answer

A)  $\frac { 8 } { 5 }$ 
B)  $- \frac { 8 } { 5 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $\varnothing$ 
A)  $\frac { 8 } { 5 }$ 
B)  $- \frac { 8 } { 5 }$ 
C)  $\frac { 4 } { 5 }$ 
D)  $\varnothing$

Question 9

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { index rationalizing } & \text { conjugate } & \text { principal square rootcube root midpoint } \
\text { complex numberlike radicals } & \text { radicand } & \text { imaginary unit } \quad \text { distance }
\end{array}$$
-A(n) -----------is a number that can be written in the form a + bi, where a and b are real numbers.

Accepted Answer

A)  distance 
B)  conjugate 
C)  complex number 
D)  radicand 
A)  distance 
B)  conjugate 
C)  complex number 
D)  radicand

Question 10

Add or subtract. Assume all variables represent positive real numbers.
-$10 \sqrt [ 4 ] { x ^ { 7 } } - 5 x \sqrt [ 4 ] { x ^ { 3 } }$

Accepted Answer

A)  $5 x \sqrt [ 4 ] { x ^ { 7 } }$ 
B)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 5 x \sqrt [ 4 ] { x ^ { 3 } }$ 
C)  $5 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $15 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
A)  $5 x \sqrt [ 4 ] { x ^ { 7 } }$ 
B)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 5 x \sqrt [ 4 ] { x ^ { 3 } }$ 
C)  $5 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $15 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$

Question 11

Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\frac { x ^ { 1 / 3 } \cdot x ^ { 1 / 4 } } { x ^ { - 1 / 7 } }$

Accepted Answer

A)  $x ^ { 37 / 84 }$ 
B)  $x ^ { 61 / 84 }$ 
C)  $\frac { 1 } { x ^ { 61 / 84 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 37 / 84 } }$ 
A)  $x ^ { 37 / 84 }$ 
B)  $x ^ { 61 / 84 }$ 
C)  $\frac { 1 } { x ^ { 61 / 84 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 37 / 84 } }$

Question 12

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive
exponents.
-$4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)$

Accepted Answer

A)  $12 x ^ { 24 / 5 } - 1$ 
B)  $12 x ^ { 24 / 5 } - 4$ 
C)  $12 x ^ { 24 / 5 } - x$ 
D)  $12 x ^ { 24 / 5 } - 4 x$ 
A)  $12 x ^ { 24 / 5 } - 1$ 
B)  $12 x ^ { 24 / 5 } - 4$ 
C)  $12 x ^ { 24 / 5 } - x$ 
D)  $12 x ^ { 24 / 5 } - 4 x$

Question 13

Multiply or divide.
-$\sqrt { 2 } \cdot \sqrt { - 8 }$

Accepted Answer

A)  $- 4 \mathrm { i }$ 
B)  $4 \mathrm { i }$ 
C)  16 
D)  $- 16$ 
A)  $- 4 \mathrm { i }$ 
B)  $4 \mathrm { i }$ 
C)  16 
D)  $- 16$

Question 14

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 30 feet from where the rope is staked down. Find the length of the rope if the altitude of the balloon is 90 feet.

Accepted Answer

A)  $120 \mathrm { ft }$ 
B)  $20 \sqrt { 3 } \mathrm { ft }$ 
C)  $30 \sqrt { 10 } \mathrm { ft }$ 
D)  $60 \sqrt { 2 } \mathrm { ft }$ 
A)  $120 \mathrm { ft }$ 
B)  $20 \sqrt { 3 } \mathrm { ft }$ 
C)  $30 \sqrt { 10 } \mathrm { ft }$ 
D)  $60 \sqrt { 2 } \mathrm { ft }$

Question 15

Find the root. Assume that all variables represent nonnegative real numbers.
-$\sqrt [ 4 ] { \frac { 81 } { x ^ { 28 } } }$

Accepted Answer

A)  $\frac { 3 } { 4 } x ^ { 7 }$ 
B)  $\frac { x ^ { 7 } } { 3 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 81 } { 4 } \mathrm { x } ^ { 7 }$ 
A)  $\frac { 3 } { 4 } x ^ { 7 }$ 
B)  $\frac { x ^ { 7 } } { 3 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 81 } { 4 } \mathrm { x } ^ { 7 }$

Question 16

Find the power of i.
-$( 4 \mathrm { i } ) ^ { 4 }$

Accepted Answer

A)  -256 
B)  256i 
C)  -256i 
D)  256 
A)  -256 
B)  256i 
C)  -256i 
D)  256

Question 17

Use the quotient rule to divide and simplify.
-$\sqrt { \frac { 32 } { 49 } }$

Accepted Answer

A)  $\frac { 4 } { 7 }$ 
B)  $16 \sqrt { 2 }$ 
C)  $\sqrt { \frac { 32 } { 7 } }$ 
D)  $\frac { 4 \sqrt { 2 } } { 7 }$ 
A)  $\frac { 4 } { 7 }$ 
B)  $16 \sqrt { 2 }$ 
C)  $\sqrt { \frac { 32 } { 7 } }$ 
D)  $\frac { 4 \sqrt { 2 } } { 7 }$

Question 18

Find the power of i.
-$\mathrm { i } ^ { 30 }$

Accepted Answer

A)  -1 
B)  1 
C)  i 
D)  -i 
A)  -1 
B)  1 
C)  i 
D)  -i

Question 19

Solve.
-$\sqrt { \mathrm { x } ^ { 2 } + 1 } = 8$

Accepted Answer

A)  $63 , - 63$ 
B)  $\sqrt { 7 }$ 
C)  $3 \sqrt { 7 } , - 3 \sqrt { 7 }$ 
D)  7 
A)  $63 , - 63$ 
B)  $\sqrt { 7 }$ 
C)  $3 \sqrt { 7 } , - 3 \sqrt { 7 }$ 
D)  7

Question 20

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt { 96 }$

Accepted Answer

A)  24 
B)  9 
C)  $4 \sqrt { 6 }$ 
D)  $6 \sqrt { 4 }$ 
A)  24 
B)  9 
C)  $4 \sqrt { 6 }$ 
D)  $6 \sqrt { 4 }$

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

Find the cube root. - $\sqrt [ 3 ] { 216 }$

Use rational exponents to write as a single radical expression. - $\sqrt [ 5 ] { 3 } \cdot \sqrt [ 3 ] { x }$

Factor the given factor from the expression. - $x ^ { 2 / 5 } ; x ^ { 4 / 5 } + 3 x ^ { 2 / 5 }$

Solve. - $\sqrt [ 3 ] { 10 x - 2 } = \sqrt [ 3 ] { x + 12 }$

Identify the domain and then graph the function. - $f ( x ) = \sqrt { x - 3 } ; \text { use the following table. }$ $Identify the domain and then graph the function. - f ( x ) = \sqrt { x - 3 } ; \text { use the following table. }$

Solve. - $\sqrt [ 3 ] { x + 3 } = \sqrt [ 3 ] { 9 x - 2 }$

Solve. - $\sqrt [ 3 ] { 5 x } = - 2$

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 -A(n) -----------is a number that can be written in the form a + bi, where a and b are real numbers.

Add or subtract. Assume all variables represent positive real numbers. - $10 \sqrt [ 4 ] { x ^ { 7 } } - 5 x \sqrt [ 4 ] { x ^ { 3 } }$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\frac { x ^ { 1 / 3 } \cdot x ^ { 1 / 4 } } { x ^ { - 1 / 7 } }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $4 x ^ { - 1 / 5 } \left( 3 x ^ { 5 } - x ^ { 1 / 5 } \right)$

Multiply or divide. - $\sqrt { 2 } \cdot \sqrt { - 8 }$

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 30 feet from where the rope is staked down. Find the length of the rope if the altitude of the balloon is 90 feet.

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 4 ] { \frac { 81 } { x ^ { 28 } } }$

Find the power of i. - $( 4 \mathrm { i } ) ^ { 4 }$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { 32 } { 49 } }$

Find the power of i. - $\mathrm { i } ^ { 30 }$

Solve. - $\sqrt { \mathrm { x } ^ { 2 } + 1 } = 8$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt { 96 }$

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

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

Find the cube root. - 2163\sqrt [ 3 ] { 216 }3216​

Use rational exponents to write as a single radical expression. - 35⋅x3\sqrt [ 5 ] { 3 } \cdot \sqrt [ 3 ] { x }53​⋅3x​

Factor the given factor from the expression. - x2/5;x4/5+3x2/5x ^ { 2 / 5 } ; x ^ { 4 / 5 } + 3 x ^ { 2 / 5 }x2/5;x4/5+3x2/5

Solve. - 10x−23=x+123\sqrt [ 3 ] { 10 x - 2 } = \sqrt [ 3 ] { x + 12 }310x−2​=3x+12​

Identify the domain and then graph the function. - f(x)=x−3; use the following table. f ( x ) = \sqrt { x - 3 } ; \text { use the following table. }f(x)=x−3​; use the following table.

Solve. - x+33=9x−23\sqrt [ 3 ] { x + 3 } = \sqrt [ 3 ] { 9 x - 2 }3x+3​=39x−2​

Solve. - 5x3=−2\sqrt [ 3 ] { 5 x } = - 235x​=−2