Question 1

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement.
-$112$

Accepted Answer

A)  $( 7 \sqrt { 7 } ) ( 2 \sqrt { 14 } )$ 
B)  $( 4 \sqrt { 3 } ) ( - 14 \sqrt { 2 } )$ 
C)  $( - 3 \sqrt { 3 } ) ( - 4 \sqrt { 8 } )$ 
D)  $( 2 \sqrt { 14 } ) ( 4 \sqrt { 14 } )$ 
A)  $( 7 \sqrt { 7 } ) ( 2 \sqrt { 14 } )$ 
B)  $( 4 \sqrt { 3 } ) ( - 14 \sqrt { 2 } )$ 
C)  $( - 3 \sqrt { 3 } ) ( - 4 \sqrt { 8 } )$ 
D)  $( 2 \sqrt { 14 } ) ( 4 \sqrt { 14 } )$

Question 2

Evaluate. $\sqrt [ 3 ] { 125 }$

Accepted Answer

The answer of Evaluate. \(\sqrt [ 3 ] { 125...

Question 3

Evaluate. $\sqrt [ 3 ] { - 64 }$

Accepted Answer

A)  $-$ 4 
B)  $-$ 8 
C)  8 
D)  4 
A)  $-$ 4 
B)  $-$ 8 
C)  8 
D)  4

Question 4

Write each of the following using positive rational exponents. Match each expression with the corresponding expression.
-$$\frac { 13 } { 11 }$$
$4 y$

Accepted Answer

A)  $4 \sqrt [ 13 ] { y ^ { 11 } }$ 
B)  $4 \sqrt [ 11 ] { y ^ { 13 } }$ 
A)  $4 \sqrt [ 13 ] { y ^ { 11 } }$ 
B)  $4 \sqrt [ 11 ] { y ^ { 13 } }$

Question 5

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $6 \sqrt [ 3 ] { 19 } ( 8 \sqrt [ 3 ] { 121 } + \sqrt [ 3 ] { 209 } )$

Accepted Answer

The answer of Find the following product and express answer...

Question 6

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 7 \sqrt { 7 } - 6 \sqrt { 5 } ) ( 6 \sqrt { 2 } + \sqrt { 11 } )$

Accepted Answer

The answer of Find the following product and express answer...

Question 7

Change the radical to simplest radical form. $- 2 \sqrt [ 3 ] { 54 }$

Accepted Answer

The answer of Change the radical to simplest radical form....

Question 8

The period of a pendulum is the time it takes to swing from one side to the other side and back. The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ where T represents the time in seconds and L the length in feet, can be used to determine the period of a pendulum (see the figure). Find the period of a 2.5-feet pendulum. Express your answer to the nearest tenth of a second.

Accepted Answer

The answer of The period of a pendulum is the...

Question 9

Simplify the numerical expression. ( 3 - 3 + 2 - 2 ) -1

Accepted Answer

A)  $\frac { 31 } { 108 }$ 
B)  $\frac { 13 } { 108 }$ 
C)  $\frac { 108 } { 31 }$ 
A)  $\frac { 31 } { 108 }$ 
B)  $\frac { 13 } { 108 }$ 
C)  $\frac { 108 } { 31 }$

Question 10

Simplify the numerical expression. ( 4 5 5 - 4 ) - 1

Accepted Answer

A)  $\frac { 625 } { 1,024 }$ 
B)  $\frac { 625 } { 3,125 }$ 
C)  $\frac { 1,024 } { 625 }$ 
A)  $\frac { 625 } { 1,024 }$ 
B)  $\frac { 625 } { 3,125 }$ 
C)  $\frac { 1,024 } { 625 }$

Question 11

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 13 } + 23 ) ( \sqrt { 13 } - 33 )$

Accepted Answer

The answer of Find the following product and express answer...

Question 12

To rationalize the denominator, all radicals are removed from the denominator by multiplying the fraction by a specific form of 1.

Accepted Answer

A) True 
 B)False

Question 13

Solve the equation. $\sqrt { 3 x + 6 } = \sqrt { 4 x + 2 }$

Accepted Answer

A)  x = 6 
B)  x = 3 
C)  x = 4 
A)  x = 6 
B)  x = 3 
C)  x = 4

Question 14

Solve the equation. $\sqrt [ 3 ] { 5 x - 1 } = \sqrt [ 3 ] { 3 - 2 x }$

Accepted Answer

The answer of Solve the equation. \(\sqrt [ 3 ]...

Question 15

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 3 } }$

Accepted Answer

The answer of Express the following expression in simplest radical...

Question 16

Change the radical to simplest radical form. $- \frac { 50 \sqrt { 8 } } { 35 \sqrt { 6 } }$

Accepted Answer

The answer of Change the radical to simplest radical form....

Question 17

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards. __________ square yards

Accepted Answer

The answer of Find, to the nearest square yard, the...

Question 18

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 3 } + 7 ) ( \sqrt { 3 } - 7 )$

Accepted Answer

The answer of Find the following product and express answer...

Question 19

A negative number in the denominator becomes positive when moved to the numerator.

Accepted Answer

A) True 
 B)False

Question 20

Perform. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

Accepted Answer

A)  $\sqrt [ 4 ] { 64 }$ 
B)  $\sqrt [ 4 ] { 512 }$ 
C)  $\sqrt [ 3 ] { 8 }$ 
D)  $\sqrt [ 4 ] { 8 }$ 
A)  $\sqrt [ 4 ] { 64 }$ 
B)  $\sqrt [ 4 ] { 512 }$ 
C)  $\sqrt [ 3 ] { 8 }$ 
D)  $\sqrt [ 4 ] { 8 }$

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $112$

Evaluate. $\sqrt [ 3 ] { 125 }$

Evaluate. $\sqrt [ 3 ] { - 64 }$

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - $\frac { 13 } { 11 }$ $4 y$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $6 \sqrt [ 3 ] { 19 } ( 8 \sqrt [ 3 ] { 121 } + \sqrt [ 3 ] { 209 } )$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 7 \sqrt { 7 } - 6 \sqrt { 5 } ) ( 6 \sqrt { 2 } + \sqrt { 11 } )$

Change the radical to simplest radical form. $- 2 \sqrt [ 3 ] { 54 }$

Simplify the numerical expression. ( 3^{- 3} + 2^{- 2}) ^-1

Simplify the numerical expression. ( 4⁵ 5^{- 4} ) ^{- 1}

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 13 } + 23 ) ( \sqrt { 13 } - 33 )$

To rationalize the denominator, all radicals are removed from the denominator by multiplying the fraction by a specific form of 1.

Solve the equation. $\sqrt { 3 x + 6 } = \sqrt { 4 x + 2 }$

Solve the equation. $\sqrt [ 3 ] { 5 x - 1 } = \sqrt [ 3 ] { 3 - 2 x }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 3 } }$

Change the radical to simplest radical form. $- \frac { 50 \sqrt { 8 } } { 35 \sqrt { 6 } }$

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards. __________ square yards

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 3 } + 7 ) ( \sqrt { 3 } - 7 )$

A negative number in the denominator becomes positive when moved to the numerator.

Perform. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 10: Exponents and Radicals

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - 112112112

Evaluate. 1253\sqrt [ 3 ] { 125 }3125​

Evaluate. −643\sqrt [ 3 ] { - 64 }3−64​

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - 1311\frac { 13 } { 11 }1113​ 4y4 y4y

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. 6193(81213+2093)6 \sqrt [ 3 ] { 19 } ( 8 \sqrt [ 3 ] { 121 } + \sqrt [ 3 ] { 209 } )6319​(83121​+3209​)

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (77−65)(62+11)( 7 \sqrt { 7 } - 6 \sqrt { 5 } ) ( 6 \sqrt { 2 } + \sqrt { 11 } )(77​−65​)(62​+11​)

Change the radical to simplest radical form. −2543- 2 \sqrt [ 3 ] { 54 }−2354​

Simplify the numerical expression. ( 3 - 3 + 2 - 2 ) -1

Simplify the numerical expression. ( 4 5 5 - 4 ) - 1

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (13+23)(13−33)( \sqrt { 13 } + 23 ) ( \sqrt { 13 } - 33 )(13​+23)(13​−33)

To rationalize the denominator, all radicals are removed from the denominator by multiplying the fraction by a specific form of 1.

Solve the equation. 3x+6=4x+2\sqrt { 3 x + 6 } = \sqrt { 4 x + 2 }3x+6​=4x+2​

Solve the equation. 5x−13=3−2x3\sqrt [ 3 ] { 5 x - 1 } = \sqrt [ 3 ] { 3 - 2 x }35x−1​=33−2x​

Express the following expression in simplest radical form. All variables represent positive real numbers. 16x33\sqrt [ 3 ] { 16 x ^ { 3 } }316x3​

Change the radical to simplest radical form. −508356- \frac { 50 \sqrt { 8 } } { 35 \sqrt { 6 } }−356​508​​

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards. __________ square yards

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (3+7)(3−7)( \sqrt { 3 } + 7 ) ( \sqrt { 3 } - 7 )(3​+7)(3​−7)

A negative number in the denominator becomes positive when moved to the numerator.

Perform. 51248\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }8​4512​​ Express answers in simplest radical form.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Multiply and simplify where possible. Match each of the expressions with the expression obtain a true statement. - $112$

Evaluate. $\sqrt [ 3 ] { 125 }$

Evaluate. $\sqrt [ 3 ] { - 64 }$

Write each of the following using positive rational exponents. Match each expression with the corresponding expression. - $\frac { 13 } { 11 }$ $4 y$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $6 \sqrt [ 3 ] { 19 } ( 8 \sqrt [ 3 ] { 121 } + \sqrt [ 3 ] { 209 } )$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 7 \sqrt { 7 } - 6 \sqrt { 5 } ) ( 6 \sqrt { 2 } + \sqrt { 11 } )$

Change the radical to simplest radical form. $- 2 \sqrt [ 3 ] { 54 }$

Simplify the numerical expression. ( 3^{- 3} + 2^{- 2}) ^-1

Simplify the numerical expression. ( 4⁵ 5^{- 4} ) ^{- 1}

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 13 } + 23 ) ( \sqrt { 13 } - 33 )$

Solve the equation. $\sqrt { 3 x + 6 } = \sqrt { 4 x + 2 }$

Solve the equation. $\sqrt [ 3 ] { 5 x - 1 } = \sqrt [ 3 ] { 3 - 2 x }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 16 x ^ { 3 } }$

Change the radical to simplest radical form. $- \frac { 50 \sqrt { 8 } } { 35 \sqrt { 6 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( \sqrt { 3 } + 7 ) ( \sqrt { 3 } - 7 )$

Perform. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.