Question 1

Find the distance between the pair of points. $( 2,1 ) , ( 5,5 )$

Accepted Answer

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

Question 2

Solve $\sqrt [ 3 ] { 7 x } = \sqrt { x }$ . Write all proposed solutions. Cross out those that are extraneous solutions.

Accepted Answer

0, 0, 49 T

Question 3

Graph $f ( x ) = - \sqrt { x - 1 } + 5$ . Give the domain and range.  
 Domain:__________ Range:___________

Accepted Answer

@#IMG-DLM&
 Domain:

Question 4

Simplify $\frac { 2 } { \sqrt { 8 } }$ by rationalizing the denominator.

Accepted Answer

A)  $\frac { 2 } { 2 \sqrt { 2 } }$ 
B)  $\frac { 1 } { \sqrt { 2 } }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { 2 \sqrt { 8 } } { 8 }$ 
A)  $\frac { 2 } { 2 \sqrt { 2 } }$ 
B)  $\frac { 1 } { \sqrt { 2 } }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { 2 \sqrt { 8 } } { 8 }$

Question 5

Perform the operation. Write the answer in a+bi  form. $( - 8 + \sqrt { - 64 } ) - ( - 2 - \sqrt { - 81 } )$

Accepted Answer

A)  $- 6 + 18 i$ 
B)  $- 9 + 20 i$ 
C)  $- 4 + 19 i$ 
D)  $- 6 + 17 i$ 
E)  $- 9 + 16 i$ 
A)  $- 6 + 18 i$ 
B)  $- 9 + 20 i$ 
C)  $- 4 + 19 i$ 
D)  $- 6 + 17 i$ 
E)  $- 9 + 16 i$

Question 6

Solve: $( 6 x - 10 ) ^ { \frac { 1 } { 3 } } = - 3$

Accepted Answer

A)  $\left\{ - \frac { 17 } { 6 } \right\}$ 
B)  $\left\{ \frac { 7 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 37 } { 6 } \right\}$ 
D)  $\left\{ \frac { 37 } { 6 } \right\}$ 
A)  $\left\{ - \frac { 17 } { 6 } \right\}$ 
B)  $\left\{ \frac { 7 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 37 } { 6 } \right\}$ 
D)  $\left\{ \frac { 37 } { 6 } \right\}$

Question 7

Find the exact length of the diagonal (in blue) of one of the faces of the cube.   Please enter your answer as a number without the units.

Accepted Answer

The answer of Find the exact length of the diagonal...

Question 8

Perform the indicated operation. Simplify, if possible. $4 \sqrt { 49 } + 2 \sqrt { 12 } - 5 \sqrt { 27 }$

Accepted Answer

A)  $17 \sqrt { 3 }$ 
B)  $7 - 11 \sqrt { 3 }$ 
C)  $28 - 11 \sqrt { 3 }$ 
D)  $28 + 6 \sqrt { 2 } - 15 \sqrt { 3 }$ 
A)  $17 \sqrt { 3 }$ 
B)  $7 - 11 \sqrt { 3 }$ 
C)  $28 - 11 \sqrt { 3 }$ 
D)  $28 + 6 \sqrt { 2 } - 15 \sqrt { 3 }$

Question 9

To obtain a __________-cube radicand in the denominator of $\frac { 3 } { \sqrt [ 3 ] { 4 } }$ , we multiply the fraction by $\frac { \sqrt [ 3 ] { 2 } } { \sqrt [ 3 ] { 2 } }$ .

Accepted Answer

The answer of To obtain a __________-cube radicand in the...

Question 10

Find the distance between the points (0,-2) and (-5,0) .

Accepted Answer

The answer of Find the distance between the points (0,-2)...

Question 11

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 225 }$

Accepted Answer

The answer of Evaluate the square root, if possible, without...

Question 12

Simplify the cube root. $\sqrt [ 3 ] { - 125 }$

Accepted Answer

The answer of Simplify the cube root. \(\sqrt [ 3...

Question 13

Simplify: $\left( 27 x ^ { 3 } y ^ { 3 } \right) ^ { - \frac { 2 } { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 9 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 1 } { 68 x ^ { 2 } y ^ { 2 } }$ 
C)  $\frac { 27 } { x ^ { 2 } y ^ { 2 } }$ 
D)  $- \frac { 9 } { x ^ { 2 } y ^ { 2 } }$ 
A)  $\frac { 1 } { 9 x ^ { 2 } y ^ { 2 } }$ 
B)  $\frac { 1 } { 68 x ^ { 2 } y ^ { 2 } }$ 
C)  $\frac { 27 } { x ^ { 2 } y ^ { 2 } }$ 
D)  $- \frac { 9 } { x ^ { 2 } y ^ { 2 } }$

Question 14

Express the number in terms of $i$ . $\sqrt { - 44 }$

Accepted Answer

The answer of Express the number in terms of $i$...

Question 15

Perform the indicated operation: $( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )$

Accepted Answer

A)  $- 2 + 7 i$ 
B)  $- 2 - 3 i$ 
C)  $95 - i$ 
D)  $- 5 + 5 i$ 
A)  $- 2 + 7 i$ 
B)  $- 2 - 3 i$ 
C)  $95 - i$ 
D)  $- 5 + 5 i$

Question 16

Simplify: $\frac { 4 \sqrt { 2 } - 1 } { \sqrt { 6 } + 3 }$

Accepted Answer

A)  $\frac { 8 \sqrt { 3 } - 12 \sqrt { 2 } - \sqrt { 6 } + 3 } { - 3 }$ 
B)  $\frac { 8 \sqrt { 3 } + 12 \sqrt { 2 } - \sqrt { 6 } - 3 } { 3 }$ 
C)  $\frac { 8 \sqrt { 3 } + 3 } { - 3 }$ 
D)  $4 \sqrt { 2 } - 1$ 
A)  $\frac { 8 \sqrt { 3 } - 12 \sqrt { 2 } - \sqrt { 6 } + 3 } { - 3 }$ 
B)  $\frac { 8 \sqrt { 3 } + 12 \sqrt { 2 } - \sqrt { 6 } - 3 } { 3 }$ 
C)  $\frac { 8 \sqrt { 3 } + 3 } { - 3 }$ 
D)  $4 \sqrt { 2 } - 1$

Question 17

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 24 V } { \pi } } \text { for } V$

Accepted Answer

A)  $V = \frac { \pi d ^ { 3 } } { 24 }$ 
B)  $V = \frac { \pi d ^ { 3 } } { 23 }$ 
C)  $V = \frac { \pi d ^ { 2 } } { 24 }$ 
D)  $V = \frac { d ^ { 3 } } { 24 \pi }$ 
E)  $V = \frac { \pi d ^ { 2 } } { 25 }$ 
A)  $V = \frac { \pi d ^ { 3 } } { 24 }$ 
B)  $V = \frac { \pi d ^ { 3 } } { 23 }$ 
C)  $V = \frac { \pi d ^ { 2 } } { 24 }$ 
D)  $V = \frac { d ^ { 3 } } { 24 \pi }$ 
E)  $V = \frac { \pi d ^ { 2 } } { 25 }$

Question 18

For the complex number $3 + 5 i$ , we call 3 the __________ part and 5 the __________ part.

Accepted Answer

The answer of For the complex number \(3 + 5...

Question 19

Rationalize the denominator. $\sqrt { \frac { 3 } { 28 } }$

Accepted Answer

A)  $\frac { \sqrt { 7 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $\frac { \sqrt { 84 } } { 14 }$ 
D)  $\frac { \sqrt { 21 } } { 14 }$ 
E)  $\frac { \sqrt { 3 } } { 2 }$ 
A)  $\frac { \sqrt { 7 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $\frac { \sqrt { 84 } } { 14 }$ 
D)  $\frac { \sqrt { 21 } } { 14 }$ 
E)  $\frac { \sqrt { 3 } } { 2 }$

Question 20

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. b=24 ft and c=145 ft  
$a =$ __________ ft

Accepted Answer

The answer of The lengths of two sides of the...

Find the distance between the pair of points. $( 2,1 ) , ( 5,5 )$

Solve $\sqrt [ 3 ] { 7 x } = \sqrt { x }$ . Write all proposed solutions. Cross out those that are extraneous solutions.

Graph $f ( x ) = - \sqrt { x - 1 } + 5$ . Give the domain and range. $Graph f ( x ) = - \sqrt { x - 1 } + 5 . Give the domain and range. Domain:____ Range:_$ Domain: Range:_____

Simplify $\frac { 2 } { \sqrt { 8 } }$ by rationalizing the denominator.

Perform the operation. Write the answer in a+bi form. $( - 8 + \sqrt { - 64 } ) - ( - 2 - \sqrt { - 81 } )$

Solve: $( 6 x - 10 ) ^ { \frac { 1 } { 3 } } = - 3$

Find the exact length of the diagonal (in blue) of one of the faces of the cube. Please enter your answer as a number without the units.

Perform the indicated operation. Simplify, if possible. $4 \sqrt { 49 } + 2 \sqrt { 12 } - 5 \sqrt { 27 }$

To obtain a __________-cube radicand in the denominator of $\frac { 3 } { \sqrt [ 3 ] { 4 } }$ , we multiply the fraction by $\frac { \sqrt [ 3 ] { 2 } } { \sqrt [ 3 ] { 2 } }$ .

Find the distance between the points (0,-2) and (-5,0) .

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 225 }$

Simplify the cube root. $\sqrt [ 3 ] { - 125 }$

Simplify: $\left( 27 x ^ { 3 } y ^ { 3 } \right) ^ { - \frac { 2 } { 3 } }$

Express the number in terms of $i$ . $\sqrt { - 44 }$

Perform the indicated operation: $( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )$

Simplify: $\frac { 4 \sqrt { 2 } - 1 } { \sqrt { 6 } + 3 }$

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 24 V } { \pi } } \text { for } V$

For the complex number $3 + 5 i$ , we call 3 the part and 5 the part.

Rationalize the denominator. $\sqrt { \frac { 3 } { 28 } }$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. b=24 ft and c=145 ft $a =$ __________ ft

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. (2,1),(5,5)( 2,1 ) , ( 5,5 )(2,1),(5,5)

Solve 7x3=x\sqrt [ 3 ] { 7 x } = \sqrt { x }37x​=x​ . Write all proposed solutions. Cross out those that are extraneous solutions.

Graph f(x)=−x−1+5f ( x ) = - \sqrt { x - 1 } + 5f(x)=−x−1​+5 . Give the domain and range. Domain:__________ Range:___________

Simplify 28\frac { 2 } { \sqrt { 8 } }8​2​ by rationalizing the denominator.

Perform the operation. Write the answer in a+bi form. (−8+−64)−(−2−−81)( - 8 + \sqrt { - 64 } ) - ( - 2 - \sqrt { - 81 } )(−8+−64​)−(−2−−81​)

Solve: (6x−10)13=−3( 6 x - 10 ) ^ { \frac { 1 } { 3 } } = - 3(6x−10)31​=−3

Find the exact length of the diagonal (in blue) of one of the faces of the cube. Please enter your answer as a number without the units.

Perform the indicated operation. Simplify, if possible. 449+212−5274 \sqrt { 49 } + 2 \sqrt { 12 } - 5 \sqrt { 27 }449​+212​−527​

To obtain a __________-cube radicand in the denominator of 343\frac { 3 } { \sqrt [ 3 ] { 4 } }34​3​ , we multiply the fraction by 2323\frac { \sqrt [ 3 ] { 2 } } { \sqrt [ 3 ] { 2 } }32​32​​ .

Find the distance between the points (0,-2) and (-5,0) .

Evaluate the square root, if possible, without using a calculator. −225- \sqrt { 225 }−225​

Simplify the cube root. −1253\sqrt [ 3 ] { - 125 }3−125​

Simplify: (27x3y3)−23\left( 27 x ^ { 3 } y ^ { 3 } \right) ^ { - \frac { 2 } { 3 } }(27x3y3)−32​

Express the number in terms of iii . −44\sqrt { - 44 }−44​

Perform the indicated operation: (5+−4)−(7−−25)( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )(5+−4​)−(7−−25​)

Simplify: 42−16+3\frac { 4 \sqrt { 2 } - 1 } { \sqrt { 6 } + 3 }6​+342​−1​

Solve the equation for the specified variable. d=24Vπ3 for Vd = \sqrt [ 3 ] { \frac { 24 V } { \pi } } \text { for } Vd=3π24V​​ for V

For the complex number 3+5i3 + 5 i3+5i , we call 3 the __________ part and 5 the __________ part.

Rationalize the denominator. 328\sqrt { \frac { 3 } { 28 } }283​​

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. b=24 ft and c=145 ft a=a =a= __________ ft

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. $( 2,1 ) , ( 5,5 )$

Solve $\sqrt [ 3 ] { 7 x } = \sqrt { x }$ . Write all proposed solutions. Cross out those that are extraneous solutions.

Graph $f ( x ) = - \sqrt { x - 1 } + 5$ . Give the domain and range. $Graph f ( x ) = - \sqrt { x - 1 } + 5 . Give the domain and range. Domain:____ Range:_$ Domain: Range:_____

Simplify $\frac { 2 } { \sqrt { 8 } }$ by rationalizing the denominator.

Perform the operation. Write the answer in a+bi form. $( - 8 + \sqrt { - 64 } ) - ( - 2 - \sqrt { - 81 } )$

Solve: $( 6 x - 10 ) ^ { \frac { 1 } { 3 } } = - 3$

Perform the indicated operation. Simplify, if possible. $4 \sqrt { 49 } + 2 \sqrt { 12 } - 5 \sqrt { 27 }$

To obtain a __________-cube radicand in the denominator of $\frac { 3 } { \sqrt [ 3 ] { 4 } }$ , we multiply the fraction by $\frac { \sqrt [ 3 ] { 2 } } { \sqrt [ 3 ] { 2 } }$ .

Evaluate the square root, if possible, without using a calculator. $- \sqrt { 225 }$

Simplify the cube root. $\sqrt [ 3 ] { - 125 }$

Simplify: $\left( 27 x ^ { 3 } y ^ { 3 } \right) ^ { - \frac { 2 } { 3 } }$

Express the number in terms of $i$ . $\sqrt { - 44 }$

Perform the indicated operation: $( 5 + \sqrt { - 4 } ) - ( 7 - \sqrt { - 25 } )$

Simplify: $\frac { 4 \sqrt { 2 } - 1 } { \sqrt { 6 } + 3 }$

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 24 V } { \pi } } \text { for } V$

For the complex number $3 + 5 i$ , we call 3 the part and 5 the part.

Rationalize the denominator. $\sqrt { \frac { 3 } { 28 } }$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. b=24 ft and c=145 ft $a =$ __________ ft