Question 1

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 8 a }$ 
B)  $6 \sqrt [ 3 ] { a }$ 
C)  $5 \sqrt [ 3 ] { a }$ 
D)  $3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }$ 
A)  $4 \sqrt [ 3 ] { 8 a }$ 
B)  $6 \sqrt [ 3 ] { a }$ 
C)  $5 \sqrt [ 3 ] { a }$ 
D)  $3 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }$ C

Question 2

Use the quotient rule to divide and simplify.
-$\sqrt { \frac { 7 } { 64 } }$

Accepted Answer

A)  $\sqrt { \frac { 7 } { 8 } }$ 
B)  $\frac { 7 } { \sqrt { 8 } }$ 
C)  $\frac { \sqrt { 7 } } { 8 }$ 
D)  $\frac { 7 } { 8 }$ 
A)  $\sqrt { \frac { 7 } { 8 } }$ 
B)  $\frac { 7 } { \sqrt { 8 } }$ 
C)  $\frac { \sqrt { 7 } } { 8 }$ 
D)  $\frac { 7 } { 8 }$ C

Question 3

Use radical notation to write the expression. Simplify if possible.
-$- 243 ^ { 1 / 5 }$

Accepted Answer

A)  $- 3$ 
B)  81 
C)  $- 27$ 
D)  243 
A)  $- 3$ 
B)  81 
C)  $- 27$ 
D)  243 A

Question 4

Solve the problem.
-Find the distance between the points $( 2 \sqrt { 2 } , - 5 )$ and $( 8 \sqrt { 2 } , - 2 )$.

Accepted Answer

A)  8 units 
B)  81 units 
C)  9 units 
D)  3 units 
A)  8 units 
B)  81 units 
C)  9 units 
D)  3 units

Question 5

Simplify. Assume that all variables represent any real number.
-$\sqrt { 100 x ^ { 2 } }$

Accepted Answer

A)  $10 \mathrm { x }$ 
B)  $- 10 x$ 
C)  $10 | x |$ 
D)  $- 10 | \mathrm { x } |$ 
A)  $10 \mathrm { x }$ 
B)  $- 10 x$ 
C)  $10 | x |$ 
D)  $- 10 | \mathrm { x } |$

Question 6

Identify the domain of f(x). Then complete the accompanying table and graph f(x).
-$f(x)=\sqrt{x+5}$

Accepted Answer

A)  $[ 5 , \infty )$
  
B)  $[ 0 , \infty )$
  
C)  $[ 0 , \infty )$
  
D)  $[ - 5 , \infty )$
  
A)  $[ 5 , \infty )$
  
B)  $[ 0 , \infty )$
  
C)  $[ 0 , \infty )$
  
D)  $[ - 5 , \infty )$

Question 7

Solve.
-$\sqrt { x + 150 } - \sqrt { x + 22 } = 8$

Accepted Answer

A)  $\varnothing$ 
B)  $- 6$ 
C)  6 
D)  7 
A)  $\varnothing$ 
B)  $- 6$ 
C)  6 
D)  7

Question 8

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt { \frac { 36 } { x } }$

Accepted Answer

A)  $\frac { 36 \sqrt { 6 x } } { x }$ 
B)  $\frac { 6 } { x }$ 
C)  $\frac { 6 \sqrt { x } } { x ^ { 2 } }$ 
D)  $\frac { 6 \sqrt { x } } { x }$ 
A)  $\frac { 36 \sqrt { 6 x } } { x }$ 
B)  $\frac { 6 } { x }$ 
C)  $\frac { 6 \sqrt { x } } { x ^ { 2 } }$ 
D)  $\frac { 6 \sqrt { x } } { x }$

Question 9

Use the quotient rule to divide and simplify.
-$\sqrt { \frac { 448 \mathrm { r } ^ { 2 } \mathrm { y } } { \mathrm { x } ^ { 4 } } }$

Accepted Answer

A)  $\frac { 8 \sqrt { 7 r ^ { 2 } y } } { x ^ { 2 } }$ 
B)  $\frac { 8 r \sqrt { 7 y } } { x ^ { 2 } }$ 
C)  $\frac { r \sqrt { 448 y } } { x ^ { 2 } }$ 
D)  $\frac { 64 \mathrm { r } \sqrt { 7 \mathrm { y } } } { \mathrm { x } ^ { 2 } }$ 
A)  $\frac { 8 \sqrt { 7 r ^ { 2 } y } } { x ^ { 2 } }$ 
B)  $\frac { 8 r \sqrt { 7 y } } { x ^ { 2 } }$ 
C)  $\frac { r \sqrt { 448 y } } { x ^ { 2 } }$ 
D)  $\frac { 64 \mathrm { r } \sqrt { 7 \mathrm { y } } } { \mathrm { x } ^ { 2 } }$

Question 10

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt { \frac { 1 } { 11 } }$

Accepted Answer

A)  $\frac { \sqrt { 11 } } { 121 }$ 
B)  1 
C)  $\sqrt { 11 }$ 
D)  $\frac { \sqrt { 11 } } { 11 }$ 
A)  $\frac { \sqrt { 11 } } { 121 }$ 
B)  1 
C)  $\sqrt { 11 }$ 
D)  $\frac { \sqrt { 11 } } { 11 }$

Question 11

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

Accepted Answer

A)  11 
B)  25 
C)  15 
D)  14 
A)  11 
B)  25 
C)  15 
D)  14

Question 12

Find the square root. Assume that all variables represent positive real numbers.
-$\sqrt { x ^ { 32 } }$

Accepted Answer

A)  $x ^ { 16 }$ 
B)  $x ^ { 32 }$ 
C)  $x ^ { 64 }$ 
D)  $x ^ { 2 }$ 
A)  $x ^ { 16 }$ 
B)  $x ^ { 32 }$ 
C)  $x ^ { 64 }$ 
D)  $x ^ { 2 }$

Question 13

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
-$\sqrt { 302 }$

Accepted Answer

A)  $17.383$ 
B)  $17.378$ 
C)  $302.000$ 
D)  $17.375$ 
A)  $17.383$ 
B)  $17.378$ 
C)  $302.000$ 
D)  $17.375$

Question 14

Solve.
-Find the perimeter of the triangle. Simplify.

Accepted Answer

A)  $17 \sqrt { 6 }$ meters 
B)  $( 42 + 7 \sqrt { 3 } )$ meters 
C)  $( 10 \sqrt { 2 } + 7 \sqrt { 3 } )$ meters 
D)  $( \sqrt { 18 } + \sqrt { 98 } + \sqrt { 147 } )$ meters 
A)  $17 \sqrt { 6 }$ meters 
B)  $( 42 + 7 \sqrt { 3 } )$ meters 
C)  $( 10 \sqrt { 2 } + 7 \sqrt { 3 } )$ meters 
D)  $( \sqrt { 18 } + \sqrt { 98 } + \sqrt { 147 } )$ meters

Question 15

Add or subtract. Assume all variables represent positive real numbers.
-$12 \sqrt [ 3 ] { 3 } + 3 \sqrt [ 3 ] { 3 }$

Accepted Answer

A)  $15 \sqrt [ 3 ] { 6 }$ 
B)  $15 \sqrt [ 3 ] { 9 }$ 
C)  $- 9 \sqrt [ 3 ] { 3 }$ 
D)  $15 \sqrt [ 3 ] { 3 }$ 
A)  $15 \sqrt [ 3 ] { 6 }$ 
B)  $15 \sqrt [ 3 ] { 9 }$ 
C)  $- 9 \sqrt [ 3 ] { 3 }$ 
D)  $15 \sqrt [ 3 ] { 3 }$

Question 16

Solve the problem.
-Find the midpoint of the line segment whose endpoints are $( - 3 , - 1 ) , ( 5 , - 6 )$.

Accepted Answer

A)  $\left( - 4 , \frac { 5 } { 2 } \right)$ 
B)  $( 2 , - 7 )$ 
C)  $\left( 1 , - \frac { 7 } { 2 } \right)$ 
D)  $( - 8,5 )$ 
A)  $\left( - 4 , \frac { 5 } { 2 } \right)$ 
B)  $( 2 , - 7 )$ 
C)  $\left( 1 , - \frac { 7 } { 2 } \right)$ 
D)  $( - 8,5 )$

Question 17

Solve the problem.
-Find the midpoint of the line segment whose endpoints are $\left( \frac { 2 } { 3 } , - 1 \right) , \left( \frac { 8 } { 3 } , \frac { 4 } { 5 } \right)$.

Accepted Answer

A)  $\left( \frac { 5 } { 3 } , - \frac { 1 } { 10 } \right)$ 
B)  $\left( - 1 , - \frac { 9 } { 10 } \right)$ 
C)  $\left( 1 , \frac { 9 } { 10 } \right)$ 
D)  $\left( \frac { 10 } { 3 } , - \frac { 1 } { 5 } \right)$ 
A)  $\left( \frac { 5 } { 3 } , - \frac { 1 } { 10 } \right)$ 
B)  $\left( - 1 , - \frac { 9 } { 10 } \right)$ 
C)  $\left( 1 , \frac { 9 } { 10 } \right)$ 
D)  $\left( \frac { 10 } { 3 } , - \frac { 1 } { 5 } \right)$

Question 18

Find the square root. Assume that all variables represent positive real numbers.
-$\sqrt { 169 }$

Accepted Answer

A)  14 
B)  not a real number 
C)  84 
D)  13 
A)  14 
B)  not a real number 
C)  84 
D)  13

Question 19

Solve.
-$\sqrt { 4 x - 3 } - 3 = 0$

Accepted Answer

A)  9 
B)  $\varnothing$ 
C)  3 
D)  $\frac { 3 } { 2 }$ 
A)  9 
B)  $\varnothing$ 
C)  3 
D)  $\frac { 3 } { 2 }$

Question 20

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 nonnegative number a is written as $\sqrt { a }$.

Accepted Answer

A)  imaginary unit 
B)  cube root 
C)  distance 
D)  principal square root 
A)  imaginary unit 
B)  cube root 
C)  distance 
D)  principal square root

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { 7 } { 64 } }$

Use radical notation to write the expression. Simplify if possible. - $- 243 ^ { 1 / 5 }$

Solve the problem. -Find the distance between the points $( 2 \sqrt { 2 } , - 5 )$ and $( 8 \sqrt { 2 } , - 2 )$ .

Simplify. Assume that all variables represent any real number. - $\sqrt { 100 x ^ { 2 } }$

Identify the domain of f(x). Then complete the accompanying table and graph f(x). - $f(x)=\sqrt{x+5}$ $Identify the domain of f(x). Then complete the accompanying table and graph f(x). - f(x)=\sqrt{x+5}$

Solve. - $\sqrt { x + 150 } - \sqrt { x + 22 } = 8$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt { \frac { 36 } { x } }$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { 448 \mathrm { r } ^ { 2 } \mathrm { y } } { \mathrm { x } ^ { 4 } } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt { \frac { 1 } { 11 } }$

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

Find the square root. Assume that all variables represent positive real numbers. - $\sqrt { x ^ { 32 } }$

Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable. - $\sqrt { 302 }$

Solve. -Find the perimeter of the triangle. Simplify.

Add or subtract. Assume all variables represent positive real numbers. - $12 \sqrt [ 3 ] { 3 } + 3 \sqrt [ 3 ] { 3 }$

Solve the problem. -Find the midpoint of the line segment whose endpoints are $( - 3 , - 1 ) , ( 5 , - 6 )$ .

Solve the problem. -Find the midpoint of the line segment whose endpoints are $\left( \frac { 2 } { 3 } , - 1 \right) , \left( \frac { 8 } { 3 } , \frac { 4 } { 5 } \right)$ .

Find the square root. Assume that all variables represent positive real numbers. - $\sqrt { 169 }$

Solve. - $\sqrt { 4 x - 3 } - 3 = 0$

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 nonnegative number a is written as $\sqrt { a }$ .

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

Add or subtract. Assume all variables represent positive real numbers. - a3+8a3\sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }3a​+38a​

Use the quotient rule to divide and simplify. - 764\sqrt { \frac { 7 } { 64 } }647​​

Use radical notation to write the expression. Simplify if possible. - −2431/5- 243 ^ { 1 / 5 }−2431/5

Solve the problem. -Find the distance between the points (22,−5)( 2 \sqrt { 2 } , - 5 )(22​,−5) and (82,−2)( 8 \sqrt { 2 } , - 2 )(82​,−2) .

Simplify. Assume that all variables represent any real number. - 100x2\sqrt { 100 x ^ { 2 } }100x2​

Identify the domain of f(x). Then complete the accompanying table and graph f(x). - f(x)=x+5f(x)=\sqrt{x+5}f(x)=x+5​

Solve. - x+150−x+22=8\sqrt { x + 150 } - \sqrt { x + 22 } = 8x+150​−x+22​=8

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 36x\sqrt { \frac { 36 } { x } }x36​​

Use the quotient rule to divide and simplify. - 448r2yx4\sqrt { \frac { 448 \mathrm { r } ^ { 2 } \mathrm { y } } { \mathrm { x } ^ { 4 } } }x4448r2y​​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 111\sqrt { \frac { 1 } { 11 } }111​​