Question 1

Simplify the expression. $16 ^ { - \frac { 3 } { 2 } }$

Accepted Answer

The answer of Simplify the expression. \(16 ^ { -...

Question 2

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 196 }$

Accepted Answer

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

Question 3

Simplify the cube root. $\sqrt [ 3 ] { - 512 }$

Accepted Answer

A)  11 
B)  -7 
C)  8 
D)  -8 
E)  7 
A)  11 
B)  -7 
C)  8 
D)  -8 
E)  7

Question 4

Simplify $- \sqrt [ 4 ] { 16 m ^ { 24 } }$ . Assume all variables represent positive real numbers.

Accepted Answer

A)  $- 2 m ^ { 6 }$ 
B)  $- 4 m ^ { 6 }$ 
C)  $- 4 m ^ { 12 }$ 
D)  not a real number 
A)  $- 2 m ^ { 6 }$ 
B)  $- 4 m ^ { 6 }$ 
C)  $- 4 m ^ { 12 }$ 
D)  not a real number

Question 5

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 5 \sqrt [ 3 ] { 2 } )$

Accepted Answer

A)  69 
B)  72 
C)  71 
D)  73 
E)  70 
A)  69 
B)  72 
C)  71 
D)  73 
E)  70

Question 6

Evaluate the expression. $\frac { 1 } { 3 }$

Accepted Answer

A)  6 
B)  216 
C)  18 
D)  24 
E)  not real 
A)  6 
B)  216 
C)  18 
D)  24 
E)  not real

Question 7

Find the missing lengths in the triangle. Give the answer to two decimal places.

Accepted Answer

A)  $x = 5.09 , y = 8.57$ 
B)  $x = 4.77 , y = 8.25$ 
C)  $x = 4.77 , y = 8.33$ 
D)  $x = 4.93 , y = 8.41$ 
E)  $x = 5.01 , y = 8.49$ 
A)  $x = 5.09 , y = 8.57$ 
B)  $x = 4.77 , y = 8.25$ 
C)  $x = 4.77 , y = 8.33$ 
D)  $x = 4.93 , y = 8.41$ 
E)  $x = 5.01 , y = 8.49$

Question 8

Solve the equation. Write all apparent solutions. Cross out those that are extraneous. $5 = 6 + \sqrt { 4 x + 83 }$

Accepted Answer

A)    , no solution 
B)  $- \frac { 41 } { 2 } ,$  
C)    , no solution 
D)  $- \frac { 41 } { 2 }$ 
E)  $- \frac { 43 } { 2 }$ 
A)    , no solution 
B)  $- \frac { 41 } { 2 } ,$  
C)    , no solution 
D)  $- \frac { 41 } { 2 }$ 
E)  $- \frac { 43 } { 2 }$

Question 9

The base of the 36-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 35 feet above the ground? Verify your result.

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 10

2+3i and 2-3i are called complex __________.

Accepted Answer

A)  elements 
B)  factors 
C)  coordinates 
D)  extensions 
E)  conjugates 
A)  elements 
B)  factors 
C)  coordinates 
D)  extensions 
E)  conjugates

Question 11

Perform the indicated operation. Simplify, if possible. $8 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }$

Accepted Answer

A)  $22 \sqrt { 3 } + 10 \sqrt { 5 }$ 
B)  $8 \sqrt { 56 }$ 
C)  $5 \sqrt { 3 } + 7 \sqrt { 7 }$ 
D)  $5 \sqrt { 2 } + 7 \sqrt { 7 }$ 
A)  $22 \sqrt { 3 } + 10 \sqrt { 5 }$ 
B)  $8 \sqrt { 56 }$ 
C)  $5 \sqrt { 3 } + 7 \sqrt { 7 }$ 
D)  $5 \sqrt { 2 } + 7 \sqrt { 7 }$

Question 12

When a radical expression is written in simplified form, each factor in the radicand is to a power __________ than the index of the radical.

Accepted Answer

The answer of When a radical expression is written in...

Question 13

Perform the multiplications. All variables represent positive real numbers. $z ^ { \frac { 3 } { 4 } } \left( z ^ { \frac { 1 } { 4 } } + z ^ { \frac { 5 } { 4 } } \right)$

Accepted Answer

The answer of Perform the multiplications. All variables represent positive...

Question 14

Simplify the expression. $\sqrt [ 4 ] { 112 }$

Accepted Answer

A)  $4 \sqrt [ 4 ] { 7 }$ 
B)  $2 + \sqrt [ 4 ] { 7 }$ 
C)  $7 \sqrt [ 4 ] { 2 }$ 
D)  $2 \sqrt [ 4 ] { 7 }$ 
E)  $49 \sqrt [ 4 ] { 2 }$ 
A)  $4 \sqrt [ 4 ] { 7 }$ 
B)  $2 + \sqrt [ 4 ] { 7 }$ 
C)  $7 \sqrt [ 4 ] { 2 }$ 
D)  $2 \sqrt [ 4 ] { 7 }$ 
E)  $49 \sqrt [ 4 ] { 2 }$

Question 15

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 7 ] { x }$ are __________ functions.

Accepted Answer

A)  cubic 
B)  radical 
C)  quadratic 
D)  rational 
E)  linear 
A)  cubic 
B)  radical 
C)  quadratic 
D)  rational 
E)  linear

Question 16

Change the exponential expression to a radical. $\left( x ^ { 3 } + y ^ { 4 } \right) ^ { \frac { 1 } { 2 } }$

Accepted Answer

The answer of Change the exponential expression to a radical....

Question 17

Evaluate the expression: $\frac { 1 } { 8 ^ { - \frac { 4 } { 3 } } }$

Accepted Answer

The answer of Evaluate the expression: \(\frac { 1 }...

Question 18

Rationalize the denominator. $\frac { \sqrt { 2 } } { \sqrt { 5 } + 3 }$

Accepted Answer

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

Question 19

The __________ number i is defined as $\sqrt { - 4 } \sqrt { - 64 }$ .

Accepted Answer

The answer of The __________ number i is defined as...

Question 20

Complete the rule for exponents. $x ^ { \frac { 1 } { n } } =$$\underline{\quad\quad}$

Accepted Answer

The rule for exponents that you're refer

Simplify the expression. $16 ^ { - \frac { 3 } { 2 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 196 }$

Simplify the cube root. $\sqrt [ 3 ] { - 512 }$

Simplify $- \sqrt [ 4 ] { 16 m ^ { 24 } }$ . Assume all variables represent positive real numbers.

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 5 \sqrt [ 3 ] { 2 } )$

Evaluate the expression. $\frac { 1 } { 3 }$

Find the missing lengths in the triangle. Give the answer to two decimal places.

Solve the equation. Write all apparent solutions. Cross out those that are extraneous. $5 = 6 + \sqrt { 4 x + 83 }$

The base of the 36-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 35 feet above the ground? Verify your result.

2+3i and 2-3i are called complex __________.

Perform the indicated operation. Simplify, if possible. $8 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }$

When a radical expression is written in simplified form, each factor in the radicand is to a power __________ than the index of the radical.

Perform the multiplications. All variables represent positive real numbers. $z ^ { \frac { 3 } { 4 } } \left( z ^ { \frac { 1 } { 4 } } + z ^ { \frac { 5 } { 4 } } \right)$

Simplify the expression. $\sqrt [ 4 ] { 112 }$

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 7 ] { x }$ are __________ functions.

Change the exponential expression to a radical. $\left( x ^ { 3 } + y ^ { 4 } \right) ^ { \frac { 1 } { 2 } }$

Evaluate the expression: $\frac { 1 } { 8 ^ { - \frac { 4 } { 3 } } }$

Rationalize the denominator. $\frac { \sqrt { 2 } } { \sqrt { 5 } + 3 }$

The __________ number i is defined as $\sqrt { - 4 } \sqrt { - 64 }$ .

Complete the rule for exponents. $x ^ { \frac { 1 } { n } } =$ $\underline{\quad\quad}$

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 the expression. 16−3216 ^ { - \frac { 3 } { 2 } }16−23​

Evaluate the square root, if possible, without using a calculator. −196\sqrt { - 196 }−196​

Simplify the cube root. −5123\sqrt [ 3 ] { - 512 }3−512​

Simplify −16m244- \sqrt [ 4 ] { 16 m ^ { 24 } }−416m24​ . Assume all variables represent positive real numbers.

Multiply and simplify, if possible. (743)(523)( 7 \sqrt [ 3 ] { 4 } ) ( 5 \sqrt [ 3 ] { 2 } )(734​)(532​)

Evaluate the expression. 13\frac { 1 } { 3 }31​

Find the missing lengths in the triangle. Give the answer to two decimal places.

Solve the equation. Write all apparent solutions. Cross out those that are extraneous. 5=6+4x+835 = 6 + \sqrt { 4 x + 83 }5=6+4x+83​

The base of the 36-foot ladder is 7 feet from the wall. Will the top reach a window ledge that is 35 feet above the ground? Verify your result.

2+3i and 2-3i are called complex __________.

Perform the indicated operation. Simplify, if possible. 848−512+5208 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }848​−512​+520​

When a radical expression is written in simplified form, each factor in the radicand is to a power __________ than the index of the radical.

Perform the multiplications. All variables represent positive real numbers. z34(z14+z54)z ^ { \frac { 3 } { 4 } } \left( z ^ { \frac { 1 } { 4 } } + z ^ { \frac { 5 } { 4 } } \right)z43​(z41​+z45​)

Simplify the expression. 1124\sqrt [ 4 ] { 112 }4112​

f(x)=xf ( x ) = \sqrt { x }f(x)=x​ and g(x)=x7g ( x ) = \sqrt [ 7 ] { x }g(x)=7x​ are __________ functions.

Change the exponential expression to a radical. (x3+y4)12\left( x ^ { 3 } + y ^ { 4 } \right) ^ { \frac { 1 } { 2 } }(x3+y4)21​

Evaluate the expression: 18−43\frac { 1 } { 8 ^ { - \frac { 4 } { 3 } } }8−34​1​

Rationalize the denominator. 25+3\frac { \sqrt { 2 } } { \sqrt { 5 } + 3 }5​+32​​

The __________ number i is defined as −4−64\sqrt { - 4 } \sqrt { - 64 }−4​−64​ .

Complete the rule for exponents. x1n=x ^ { \frac { 1 } { n } } =xn1​=‾\underline{\quad\quad}​

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 the expression. $16 ^ { - \frac { 3 } { 2 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { - 196 }$

Simplify the cube root. $\sqrt [ 3 ] { - 512 }$

Simplify $- \sqrt [ 4 ] { 16 m ^ { 24 } }$ . Assume all variables represent positive real numbers.

Multiply and simplify, if possible. $( 7 \sqrt [ 3 ] { 4 } ) ( 5 \sqrt [ 3 ] { 2 } )$

Evaluate the expression. $\frac { 1 } { 3 }$

Solve the equation. Write all apparent solutions. Cross out those that are extraneous. $5 = 6 + \sqrt { 4 x + 83 }$

Perform the indicated operation. Simplify, if possible. $8 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }$

Perform the multiplications. All variables represent positive real numbers. $z ^ { \frac { 3 } { 4 } } \left( z ^ { \frac { 1 } { 4 } } + z ^ { \frac { 5 } { 4 } } \right)$

Simplify the expression. $\sqrt [ 4 ] { 112 }$

$f ( x ) = \sqrt { x }$ and $g ( x ) = \sqrt [ 7 ] { x }$ are __________ functions.

Change the exponential expression to a radical. $\left( x ^ { 3 } + y ^ { 4 } \right) ^ { \frac { 1 } { 2 } }$

Evaluate the expression: $\frac { 1 } { 8 ^ { - \frac { 4 } { 3 } } }$

Rationalize the denominator. $\frac { \sqrt { 2 } } { \sqrt { 5 } + 3 }$

The __________ number i is defined as $\sqrt { - 4 } \sqrt { - 64 }$ .

Complete the rule for exponents. $x ^ { \frac { 1 } { n } } =$ $\underline{\quad\quad}$