Question 1

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }$

Accepted Answer

A)  $4 x \sqrt [ 3 ] { 7 }$ 
B)  $4 \sqrt [ 3 ] { 7 x }$ 
C)  $\sqrt [ 3 ] { 10 x }$ 
D)  $4 + \sqrt [ 3 ] { 7 x }$ 
E)  $\sqrt [ 3 ] { 7 x }$ 
A)  $4 x \sqrt [ 3 ] { 7 }$ 
B)  $4 \sqrt [ 3 ] { 7 x }$ 
C)  $\sqrt [ 3 ] { 10 x }$ 
D)  $4 + \sqrt [ 3 ] { 7 x }$ 
E)  $\sqrt [ 3 ] { 7 x }$

Question 2

A curved road will accommodate traffic traveling s mph if the radius of the curve is r feet, according to the formula $s = 3 \sqrt { r }$ . If engineers expect 55-mph traffic, what radius should they specify? Give the result to the nearest foot.

Accepted Answer

A)  $r = 345 \mathrm { f }$ 
B)  $r = 339 \mathrm { f }$ 
C)  $r = 351 \mathrm { ft }$ 
D)  $r = 336 \mathrm { t }$ 
E)  $r = 342 \mathrm { ft }$ 
A)  $r = 345 \mathrm { f }$ 
B)  $r = 339 \mathrm { f }$ 
C)  $r = 351 \mathrm { ft }$ 
D)  $r = 336 \mathrm { t }$ 
E)  $r = 342 \mathrm { ft }$

Question 3

Simplify: $- \sqrt [ 3 ] { - 125 x ^ { 9 } }$

Accepted Answer

A)  $- 4 x ^ { 3 }$ 
B)  $- 5 x ^ { 3 }$ 
C)  $5 x ^ { 3 }$ 
D)  not a real number 
A)  $- 4 x ^ { 3 }$ 
B)  $- 5 x ^ { 3 }$ 
C)  $5 x ^ { 3 }$ 
D)  not a real number

Question 4

If one leg of an isosceles right triangle is 2 feet, find the length of the hypotenuse.

Accepted Answer

The answer of If one leg of an isosceles right...

Question 5

What is the formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ ?

Accepted Answer

A)  $d = \sqrt { \left( x _ { 2 } + x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } + y _ { 1 } \right) ^ { 2 } }$ 
B)  $d = \sqrt { \left( x _ { 2 } + x _ { 1 } \right) ^ { 2 } - \left( y _ { 2 } + y _ { 1 } \right) ^ { 2 } }$ 
C)  $d = \sqrt { \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 } }$ 
D)  $d = \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 }$ 
E)  $d = \sqrt { \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } - \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 } }$ 
A)  $d = \sqrt { \left( x _ { 2 } + x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } + y _ { 1 } \right) ^ { 2 } }$ 
B)  $d = \sqrt { \left( x _ { 2 } + x _ { 1 } \right) ^ { 2 } - \left( y _ { 2 } + y _ { 1 } \right) ^ { 2 } }$ 
C)  $d = \sqrt { \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 } }$ 
D)  $d = \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } + \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 }$ 
E)  $d = \sqrt { \left( x _ { 2 } - x _ { 1 } \right) ^ { 2 } - \left( y _ { 2 } - y _ { 1 } \right) ^ { 2 } }$

Question 6

Rationalize the denominator. All variables represent positive real numbers. $\frac { \sqrt { 35 x ^ { 6 } } } { \sqrt { 5 x ^ { 6 } y } }$

Accepted Answer

The answer of Rationalize the denominator. All variables represent positive...

Question 7

Simplify: $\left( i ^ { 390 } \right) ^ { i ^ { 480 } }$

Accepted Answer

The answer of Simplify: \(\left( i ^ { 390 }...

Question 8

Rationalize the denominator: $\frac { 6 } { 2 \sqrt { 3 } - 1 }$

Accepted Answer

A)  $\frac { 12 \sqrt { 3 } + 6 } { 11 }$ 
B)  $\frac { 12 \sqrt { 3 } + 1 } { 11 }$ 
C)  $\frac { 12 \sqrt { 3 } + 6 } { 17 }$ 
D)  none of these 
A)  $\frac { 12 \sqrt { 3 } + 6 } { 11 }$ 
B)  $\frac { 12 \sqrt { 3 } + 1 } { 11 }$ 
C)  $\frac { 12 \sqrt { 3 } + 6 } { 17 }$ 
D)  none of these

Question 9

The denominator of $\frac { 7 } { \sqrt { 5 } }$ is a(n) __________ number.

Accepted Answer

A)  rational 
B)  whole 
C)  irrational 
D)  natural 
A)  rational 
B)  whole 
C)  irrational 
D)  natural

Question 10

In the exponential expression $27 ^ { \frac { 6 } { 5 } }$ , 27 is the __________ and $\frac { 6 } { 5 }$ is the __________.

Accepted Answer

The answer of In the exponential expression \(27 ^ {...

Question 11

Rationalize the denominator. $\sqrt { \frac { 7 } { 12 } }$

Accepted Answer

The answer of Rationalize the denominator. \(\sqrt { \frac {...

Question 12

$6 + 4 i$ and $6 - 4 i$ are called complex __________.

Accepted Answer

The answer of $6 + 4 i$ and \(6 -...

Question 13

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

Accepted Answer

A)  -9 
B)  -6 
C)  -3 
D)  $\sqrt [ 3 ] { 27 }$ 
E)  not real 
A)  -9 
B)  -6 
C)  -3 
D)  $\sqrt [ 3 ] { 27 }$ 
E)  not real

Question 14

To __________ the denominator of $\frac { 3 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Accepted Answer

The answer of To __________ the denominator of \(\frac {...

Question 15

Multiply and simplify, if possible. $( \sqrt { 5 } + 1 ) ( \sqrt { 5 } - 9 )$

Accepted Answer

The answer of Multiply and simplify, if possible. \(( \sqrt...

Question 16

Simplify the expression. $i ^ { 28 }$

Accepted Answer

A)  $1$ 
B)  $- i$ 
C)  $\sqrt { i }$ 
D)  $- 1$ 
E)  $i$ 
A)  $1$ 
B)  $- i$ 
C)  $\sqrt { i }$ 
D)  $- 1$ 
E)  $i$

Question 17

Multiply. Write the answer in the form a+bi . $( 4 + 7 i ) ^ { 2 }$

Accepted Answer

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

Question 18

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 12 } ) ^ { 2 }$

Accepted Answer

A)  108 
B)  105 
C)  107 
D)  109 
E)  106 
A)  108 
B)  105 
C)  107 
D)  109 
E)  106

Question 19

Divide. Write the answer in the form $a + b i$ . $\frac { 26 } { 5 - i }$

Accepted Answer

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

Question 20

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 8 V } { \pi } } \text { for } V$

Accepted Answer

The answer of Solve the equation for the specified variable....

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }$

Simplify: $- \sqrt [ 3 ] { - 125 x ^ { 9 } }$

If one leg of an isosceles right triangle is 2 feet, find the length of the hypotenuse.

What is the formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ ?

Rationalize the denominator. All variables represent positive real numbers. $\frac { \sqrt { 35 x ^ { 6 } } } { \sqrt { 5 x ^ { 6 } y } }$

Simplify: $\left( i ^ { 390 } \right) ^ { i ^ { 480 } }$

Rationalize the denominator: $\frac { 6 } { 2 \sqrt { 3 } - 1 }$

The denominator of $\frac { 7 } { \sqrt { 5 } }$ is a(n) __________ number.

In the exponential expression $27 ^ { \frac { 6 } { 5 } }$ , 27 is the and $\frac { 6 } { 5 }$ is the .

Rationalize the denominator. $\sqrt { \frac { 7 } { 12 } }$

$6 + 4 i$ and $6 - 4 i$ are called complex __________.

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

To __________ the denominator of $\frac { 3 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Multiply and simplify, if possible. $( \sqrt { 5 } + 1 ) ( \sqrt { 5 } - 9 )$

Simplify the expression. $i ^ { 28 }$

Multiply. Write the answer in the form a+bi . $( 4 + 7 i ) ^ { 2 }$

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 12 } ) ^ { 2 }$

Divide. Write the answer in the form $a + b i$ . $\frac { 26 } { 5 - i }$

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 8 V } { \pi } } \text { for } V$

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

Simplify by combining like radicals. The variable represents a positive real number. 189x3+7x3\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }3189x​+37x​

A curved road will accommodate traffic traveling s mph if the radius of the curve is r feet, according to the formula s=3rs = 3 \sqrt { r }s=3r​ . If engineers expect 55-mph traffic, what radius should they specify? Give the result to the nearest foot.

Simplify: −−125x93- \sqrt [ 3 ] { - 125 x ^ { 9 } }−3−125x9​

If one leg of an isosceles right triangle is 2 feet, find the length of the hypotenuse.

What is the formula to find the distance d between two points (x1,y1)\left( x _ { 1 } , y _ { 1 } \right)(x1​,y1​) and (x2,y2)\left( x _ { 2 } , y _ { 2 } \right)(x2​,y2​) ?

Rationalize the denominator. All variables represent positive real numbers. 35x65x6y\frac { \sqrt { 35 x ^ { 6 } } } { \sqrt { 5 x ^ { 6 } y } }5x6y​35x6​​

Simplify: (i390)i480\left( i ^ { 390 } \right) ^ { i ^ { 480 } }(i390)i480

Rationalize the denominator: 623−1\frac { 6 } { 2 \sqrt { 3 } - 1 }23​−16​

The denominator of 75\frac { 7 } { \sqrt { 5 } }5​7​ is a(n) __________ number.

In the exponential expression 276527 ^ { \frac { 6 } { 5 } }2756​ , 27 is the __________ and 65\frac { 6 } { 5 }56​ is the __________.

Rationalize the denominator. 712\sqrt { \frac { 7 } { 12 } }127​​

6+4i6 + 4 i6+4i and 6−4i6 - 4 i6−4i are called complex __________.

Evaluate the expression. −2713- 27 ^ { \frac { 1 } { 3 } }−2731​

To __________ the denominator of 36\frac { 3 } { \sqrt { 6 } }6​3​ , we multiply the fraction by 66\frac { \sqrt { 6 } } { \sqrt { 6 } }6​6​​ .

Multiply and simplify, if possible. (5+1)(5−9)( \sqrt { 5 } + 1 ) ( \sqrt { 5 } - 9 )(5​+1)(5​−9)

Simplify the expression. i28i ^ { 28 }i28

Multiply. Write the answer in the form a+bi . (4+7i)2( 4 + 7 i ) ^ { 2 }(4+7i)2

Square the quantity and simplify the result, if possible. (312)2( 3 \sqrt { 12 } ) ^ { 2 }(312​)2

Divide. Write the answer in the form a+bia + b ia+bi . 265−i\frac { 26 } { 5 - i }5−i26​

Solve the equation for the specified variable. d=8Vπ3 for Vd = \sqrt [ 3 ] { \frac { 8 V } { \pi } } \text { for } Vd=3π8V​​ for V

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

Simplify by combining like radicals. The variable represents a positive real number. $\sqrt [ 3 ] { 189 x } + \sqrt [ 3 ] { 7 x }$

Simplify: $- \sqrt [ 3 ] { - 125 x ^ { 9 } }$

What is the formula to find the distance d between two points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ ?

Rationalize the denominator. All variables represent positive real numbers. $\frac { \sqrt { 35 x ^ { 6 } } } { \sqrt { 5 x ^ { 6 } y } }$

Simplify: $\left( i ^ { 390 } \right) ^ { i ^ { 480 } }$

Rationalize the denominator: $\frac { 6 } { 2 \sqrt { 3 } - 1 }$

The denominator of $\frac { 7 } { \sqrt { 5 } }$ is a(n) __________ number.

In the exponential expression $27 ^ { \frac { 6 } { 5 } }$ , 27 is the and $\frac { 6 } { 5 }$ is the .

Rationalize the denominator. $\sqrt { \frac { 7 } { 12 } }$

$6 + 4 i$ and $6 - 4 i$ are called complex __________.

Evaluate the expression. $- 27 ^ { \frac { 1 } { 3 } }$

To __________ the denominator of $\frac { 3 } { \sqrt { 6 } }$ , we multiply the fraction by $\frac { \sqrt { 6 } } { \sqrt { 6 } }$ .

Multiply and simplify, if possible. $( \sqrt { 5 } + 1 ) ( \sqrt { 5 } - 9 )$

Simplify the expression. $i ^ { 28 }$

Multiply. Write the answer in the form a+bi . $( 4 + 7 i ) ^ { 2 }$

Square the quantity and simplify the result, if possible. $( 3 \sqrt { 12 } ) ^ { 2 }$

Divide. Write the answer in the form $a + b i$ . $\frac { 26 } { 5 - i }$

Solve the equation for the specified variable. $d = \sqrt [ 3 ] { \frac { 8 V } { \pi } } \text { for } V$