Question 1

Find the distance between the pair of points. $( - 1 , - 7 ) , ( 5,1 )$

Accepted Answer

The answer of Find the distance between the pair of...

Question 2

Find the distance between the pair of points. $( - 1,6 ) , ( - 7 , - 8 )$

Accepted Answer

The answer of Find the distance between the pair of...

Question 3

Perform the indicated operation: $( - 5 + 3 i ) - ( 3 - i )$

Accepted Answer

A)  $- 8 + 2 i$ 
B)  $2 + 2 i$ 
C)  $- 2 + 4 i$ 
D)  $- 8 + 4 i$ 
A)  $- 8 + 2 i$ 
B)  $2 + 2 i$ 
C)  $- 2 + 4 i$ 
D)  $- 8 + 4 i$

Question 4

Rationalize the denominator. $\frac { \sqrt { 11 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 11 } }$

Accepted Answer

A)  $\frac { 12 - 2 \sqrt { 22 } } { 9 }$ 
B)  $\frac { 9 - 2 \sqrt { 22 } } { 9 }$ 
C)  $\frac { 11 - 2 \sqrt { 22 } } { 9 }$ 
D)  $\frac { 13 - 2 \sqrt { 22 } } { 9 }$ 
E)  $\frac { 10 - 2 \sqrt { 22 } } { 9 }$ 
A)  $\frac { 12 - 2 \sqrt { 22 } } { 9 }$ 
B)  $\frac { 9 - 2 \sqrt { 22 } } { 9 }$ 
C)  $\frac { 11 - 2 \sqrt { 22 } } { 9 }$ 
D)  $\frac { 13 - 2 \sqrt { 22 } } { 9 }$ 
E)  $\frac { 10 - 2 \sqrt { 22 } } { 9 }$

Question 5

Solve: $\sqrt { 2 x - 7 } - 2 = 3$

Accepted Answer

A)  $\left\{ \frac { 44 } { 3 } \right\}$ 
B)  $\left\{ \frac { 33 } { 4 } \right\}$ 
C)  $\{ 23 \}$ 
D)  $\{ 16 \}$ 
A)  $\left\{ \frac { 44 } { 3 } \right\}$ 
B)  $\left\{ \frac { 33 } { 4 } \right\}$ 
C)  $\{ 23 \}$ 
D)  $\{ 16 \}$

Question 6

The __________ number i is defined as $i = \sqrt { - 1 }$ .

Accepted Answer

A)  real 
B)  rational 
C)  integer 
D)  imaginary 
E)  complex 
A)  real 
B)  rational 
C)  integer 
D)  imaginary 
E)  complex

Question 7

Solve: $\sqrt { 2 x + 6 } = \sqrt { 5 x } - 1$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ - 5 \}$ 
D)  no solution 
A)  $\{ 2 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ - 5 \}$ 
D)  no solution

Question 8

Multiply. Write the answer in the form a+bi   $( 1 - \sqrt { - 9 } ) ( 7 + \sqrt { - 4 } )$

Accepted Answer

The answer of Multiply. Write the answer in the form...

Question 9

In the radical expression $\sqrt [ 3 ] { 8 x ^ { 3 } }$ , $8 x ^ { 3 }$ is the __________.

Accepted Answer

The answer of In the radical expression \(\sqrt [ 3...

Question 10

Use the distance formula to show that a triangle with vertices (-2,2) , (2,7) , and (6,2) is isosceles.

Accepted Answer

Distance between (-2,2) and (2

Question 11

For the complex number 4+5i , we call 4 the __________ part.

Accepted Answer

A)  complex 
B)  real 
C)  imaginary 
D)  positive 
E)  integer 
A)  complex 
B)  real 
C)  imaginary 
D)  positive 
E)  integer

Question 12

Express the number in terms of i . $\sqrt { - 40 }$

Accepted Answer

A)  -40i 
B)  -$2 \sqrt { 10 } i$ 
C)  40i 
D)  $2 \sqrt { 10 } i$ 
E)  10i 
A)  -40i 
B)  -$2 \sqrt { 10 } i$ 
C)  40i 
D)  $2 \sqrt { 10 } i$ 
E)  10i

Question 13

Simplify the expression. All variables represent positive real numbers. $- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }$

Accepted Answer

A)  $- \frac { 1 } { 64 x ^ { 3 } }$ 
B)  $- \frac { 16 } { x ^ { 3 } }$ 
C)  $- \frac { 64 } { x ^ { 3 } }$ 
D)  $- \frac { x ^ { 2 } } { 64 }$ 
E)  $- \frac { x ^ { 3 } } { 64 }$ 
A)  $- \frac { 1 } { 64 x ^ { 3 } }$ 
B)  $- \frac { 16 } { x ^ { 3 } }$ 
C)  $- \frac { 64 } { x ^ { 3 } }$ 
D)  $- \frac { x ^ { 2 } } { 64 }$ 
E)  $- \frac { x ^ { 3 } } { 64 }$

Question 14

Rationalize the denominator. $\frac { 9 } { \sqrt [ 3 ] { 81 } }$

Accepted Answer

A)  $\sqrt [ 3 ] { 9 }$ 
B)  $\frac { \sqrt { 9 } } { 9 }$ 
C)  $\frac { 9 \sqrt [ 3 ] { 9 } } { 81 }$ 
D)  $\sqrt [ 3 ] { 81 }$ 
E)  $\sqrt { 9 }$ 
A)  $\sqrt [ 3 ] { 9 }$ 
B)  $\frac { \sqrt { 9 } } { 9 }$ 
C)  $\frac { 9 \sqrt [ 3 ] { 9 } } { 81 }$ 
D)  $\sqrt [ 3 ] { 81 }$ 
E)  $\sqrt { 9 }$

Question 15

Find the distance between the pair of points. $( 1,3 ) , ( 9,9 )$

Accepted Answer

A)  6 
B)  7 
C)  10 
D)  8 
E)  9 
A)  6 
B)  7 
C)  10 
D)  8 
E)  9

Question 16

Multiply and simplify, if possible. $\sqrt { 5 } ( 9 \sqrt { 15 } + 4 \sqrt { 7 } )$

Accepted Answer

A)  $45 \sqrt { 35 } + 4 \sqrt { 3 }$ 
B)  $4 \sqrt { 35 }$ 
C)  $45 \sqrt { 3 } - 4 \sqrt { 35 }$ 
D)  $45 \sqrt { 3 } + 4 \sqrt { 35 }$ 
E)  $45 \sqrt { 3 }$ 
A)  $45 \sqrt { 35 } + 4 \sqrt { 3 }$ 
B)  $4 \sqrt { 35 }$ 
C)  $45 \sqrt { 3 } - 4 \sqrt { 35 }$ 
D)  $45 \sqrt { 3 } + 4 \sqrt { 35 }$ 
E)  $45 \sqrt { 3 }$

Question 17

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt [ 3 ] { x } + 2$

Accepted Answer

A)  $D = ( - \infty , 2 ) ; R = ( - \infty , 2 )$ 
B)  $D = [ 2 , \infty ) ; R = [ - \infty , 2 )$ 
C)  $D = ( 2 , \infty ) ; R = ( 2 , \infty )$ 
D)  $D = [ 1 , \infty ) ; R = [ - \infty , 1 )$ 
E)  $D = ( - \infty , \infty ) ; R = ( - \infty , \infty )$ 
A)  $D = ( - \infty , 2 ) ; R = ( - \infty , 2 )$ 
B)  $D = [ 2 , \infty ) ; R = [ - \infty , 2 )$ 
C)  $D = ( 2 , \infty ) ; R = ( 2 , \infty )$ 
D)  $D = [ 1 , \infty ) ; R = [ - \infty , 1 )$ 
E)  $D = ( - \infty , \infty ) ; R = ( - \infty , \infty )$

Question 18

Simplify the cube root. $\sqrt [ 3 ] { - 27 a ^ { 3 } }$

Accepted Answer

A)  -3a 
B)  $- 3 a ^ { 3 }$ 
C)  -6a 
D)  3|a| 
E)   6|a| 
A)  -3a 
B)  $- 3 a ^ { 3 }$ 
C)  -6a 
D)  3|a| 
E)   6|a|

Question 19

Multiply and simplify, if possible. All variables represent positive real numbers. $4 \sqrt { 5 t } \left( 2 \sqrt { 5 t } + 2 \sqrt { 7 t ^ { 2 } } \right)$

Accepted Answer

The answer of Multiply and simplify, if possible. All variables...

Question 20

Simplify by combining like radicals. The variable represents a positive real number. $2 \sqrt { 2 x } + 7 \sqrt { 2 x }$

Accepted Answer

The answer of Simplify by combining like radicals. The variable...

Find the distance between the pair of points. $( - 1 , - 7 ) , ( 5,1 )$

Find the distance between the pair of points. $( - 1,6 ) , ( - 7 , - 8 )$

Perform the indicated operation: $( - 5 + 3 i ) - ( 3 - i )$

Rationalize the denominator. $\frac { \sqrt { 11 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 11 } }$

Solve: $\sqrt { 2 x - 7 } - 2 = 3$

The __________ number i is defined as $i = \sqrt { - 1 }$ .

Solve: $\sqrt { 2 x + 6 } = \sqrt { 5 x } - 1$

Multiply. Write the answer in the form a+bi $( 1 - \sqrt { - 9 } ) ( 7 + \sqrt { - 4 } )$

In the radical expression $\sqrt [ 3 ] { 8 x ^ { 3 } }$ , $8 x ^ { 3 }$ is the __________.

Use the distance formula to show that a triangle with vertices (-2,2) , (2,7) , and (6,2) is isosceles.

For the complex number 4+5i , we call 4 the __________ part.

Express the number in terms of i . $\sqrt { - 40 }$

Simplify the expression. All variables represent positive real numbers. $- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }$

Rationalize the denominator. $\frac { 9 } { \sqrt [ 3 ] { 81 } }$

Find the distance between the pair of points. $( 1,3 ) , ( 9,9 )$

Multiply and simplify, if possible. $\sqrt { 5 } ( 9 \sqrt { 15 } + 4 \sqrt { 7 } )$

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt [ 3 ] { x } + 2$

Simplify the cube root. $\sqrt [ 3 ] { - 27 a ^ { 3 } }$

Multiply and simplify, if possible. All variables represent positive real numbers. $4 \sqrt { 5 t } \left( 2 \sqrt { 5 t } + 2 \sqrt { 7 t ^ { 2 } } \right)$

Simplify by combining like radicals. The variable represents a positive real number. $2 \sqrt { 2 x } + 7 \sqrt { 2 x }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 7: Radical Expressions and Equations

Find the distance between the pair of points. (−1,−7),(5,1)( - 1 , - 7 ) , ( 5,1 )(−1,−7),(5,1)

Find the distance between the pair of points. (−1,6),(−7,−8)( - 1,6 ) , ( - 7 , - 8 )(−1,6),(−7,−8)

Perform the indicated operation: (−5+3i)−(3−i)( - 5 + 3 i ) - ( 3 - i )(−5+3i)−(3−i)

Rationalize the denominator. 11−22+11\frac { \sqrt { 11 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 11 } }2​+11​11​−2​​

Solve: 2x−7−2=3\sqrt { 2 x - 7 } - 2 = 32x−7​−2=3

The __________ number i is defined as i=−1i = \sqrt { - 1 }i=−1​ .

Solve: 2x+6=5x−1\sqrt { 2 x + 6 } = \sqrt { 5 x } - 12x+6​=5x​−1

Multiply. Write the answer in the form a+bi (1−−9)(7+−4)( 1 - \sqrt { - 9 } ) ( 7 + \sqrt { - 4 } )(1−−9​)(7+−4​)

In the radical expression 8x33\sqrt [ 3 ] { 8 x ^ { 3 } }38x3​ , 8x38 x ^ { 3 }8x3 is the __________.

Use the distance formula to show that a triangle with vertices (-2,2) , (2,7) , and (6,2) is isosceles.

For the complex number 4+5i , we call 4 the __________ part.

Express the number in terms of i . −40\sqrt { - 40 }−40​

Simplify the expression. All variables represent positive real numbers. −(16x2)−32- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }−(16x2)−23​

Rationalize the denominator. 9813\frac { 9 } { \sqrt [ 3 ] { 81 } }381​9​

Find the distance between the pair of points. (1,3),(9,9)( 1,3 ) , ( 9,9 )(1,3),(9,9)

Multiply and simplify, if possible. 5(915+47)\sqrt { 5 } ( 9 \sqrt { 15 } + 4 \sqrt { 7 } )5​(915​+47​)

Find the domain and range of the function f(x)f ( x )f(x) . f(x)=x3+2f ( x ) = \sqrt [ 3 ] { x } + 2f(x)=3x​+2

Simplify the cube root. −27a33\sqrt [ 3 ] { - 27 a ^ { 3 } }3−27a3​

Multiply and simplify, if possible. All variables represent positive real numbers. 45t(25t+27t2)4 \sqrt { 5 t } \left( 2 \sqrt { 5 t } + 2 \sqrt { 7 t ^ { 2 } } \right)45t​(25t​+27t2​)

Simplify by combining like radicals. The variable represents a positive real number. 22x+72x2 \sqrt { 2 x } + 7 \sqrt { 2 x }22x​+72x​

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Find the distance between the pair of points. $( - 1 , - 7 ) , ( 5,1 )$

Find the distance between the pair of points. $( - 1,6 ) , ( - 7 , - 8 )$

Perform the indicated operation: $( - 5 + 3 i ) - ( 3 - i )$

Rationalize the denominator. $\frac { \sqrt { 11 } - \sqrt { 2 } } { \sqrt { 2 } + \sqrt { 11 } }$

Solve: $\sqrt { 2 x - 7 } - 2 = 3$

The __________ number i is defined as $i = \sqrt { - 1 }$ .

Solve: $\sqrt { 2 x + 6 } = \sqrt { 5 x } - 1$

Multiply. Write the answer in the form a+bi $( 1 - \sqrt { - 9 } ) ( 7 + \sqrt { - 4 } )$

In the radical expression $\sqrt [ 3 ] { 8 x ^ { 3 } }$ , $8 x ^ { 3 }$ is the __________.

Express the number in terms of i . $\sqrt { - 40 }$

Simplify the expression. All variables represent positive real numbers. $- \left( 16 x ^ { 2 } \right) ^ { - \frac { 3 } { 2 } }$

Rationalize the denominator. $\frac { 9 } { \sqrt [ 3 ] { 81 } }$

Find the distance between the pair of points. $( 1,3 ) , ( 9,9 )$

Multiply and simplify, if possible. $\sqrt { 5 } ( 9 \sqrt { 15 } + 4 \sqrt { 7 } )$

Find the domain and range of the function $f ( x )$ . $f ( x ) = \sqrt [ 3 ] { x } + 2$

Simplify the cube root. $\sqrt [ 3 ] { - 27 a ^ { 3 } }$

Multiply and simplify, if possible. All variables represent positive real numbers. $4 \sqrt { 5 t } \left( 2 \sqrt { 5 t } + 2 \sqrt { 7 t ^ { 2 } } \right)$

Simplify by combining like radicals. The variable represents a positive real number. $2 \sqrt { 2 x } + 7 \sqrt { 2 x }$