Question 1

Simplify the numerical expression. 5 - 2 + 2 - 2

Accepted Answer

A)  $\frac { 100 } { 29 }$ 
B)  $\frac { 20 } { 29 }$ 
C)  $\frac { 29 } { 100 }$ 
A)  $\frac { 100 } { 29 }$ 
B)  $\frac { 20 } { 29 }$ 
C)  $\frac { 29 } { 100 }$

Question 2

Solve the equation. $\sqrt { 5 x + 3 } = \sqrt { 9 x - 3 }$

Accepted Answer

A)  x = 3 
B)  x = 5 
C)  x = 1.5 
A)  x = 3 
B)  x = 5 
C)  x = 1.5

Question 3

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 81 x ^ { 6 } y ^ { 8 } }$

Accepted Answer

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

Question 4

Find the indicated product. Express final results using positive integral exponents only. (3 xy  - 2)(8 x - 3 y 7)

Accepted Answer

A)  $\frac { x ^ { 2 } } { 24 y ^ { 5 } }$ 
B)  $24 x ^ { 2 } y ^ { 5 }$ 
C)  $\frac { 24 y ^ { 5 } } { x ^ { 2 } }$ 
A)  $\frac { x ^ { 2 } } { 24 y ^ { 5 } }$ 
B)  $24 x ^ { 2 } y ^ { 5 }$ 
C)  $\frac { 24 y ^ { 5 } } { x ^ { 2 } }$

Question 5

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 19 } - 9 \sqrt { 323 } ) ( 3 \sqrt { 4,913 } + \sqrt { 323 } )$

Accepted Answer

A)  $408 \sqrt { 323 } - 152 \sqrt { 19 } - 7,803 \sqrt { 17 } + 2,907$ 
B)  $408 \sqrt { 323 } + 152 \sqrt { 17 } - 7,803 \sqrt { 19 } - 2,907 \sqrt { 4,913 }$ 
C)  $24 \sqrt { 17 } + 8 \sqrt { 19 } - 2,907$ 
D)  $408 \sqrt { 323 } + 152 \sqrt { 17 } - 7,803 \sqrt { 19 } - 2,907$ 
E)  $- 408 \sqrt { 323 } - 152 \sqrt { 17 } + 7,803 \sqrt { 19 } + 2,907$ 
A)  $408 \sqrt { 323 } - 152 \sqrt { 19 } - 7,803 \sqrt { 17 } + 2,907$ 
B)  $408 \sqrt { 323 } + 152 \sqrt { 17 } - 7,803 \sqrt { 19 } - 2,907 \sqrt { 4,913 }$ 
C)  $24 \sqrt { 17 } + 8 \sqrt { 19 } - 2,907$ 
D)  $408 \sqrt { 323 } + 152 \sqrt { 17 } - 7,803 \sqrt { 19 } - 2,907$ 
E)  $- 408 \sqrt { 323 } - 152 \sqrt { 17 } + 7,803 \sqrt { 19 } + 2,907$

Question 6

Evaluate. $\sqrt [ 6 ] { 2 ^ { 6 } }$

Accepted Answer

A)  -4 
B)  8 
C)  2 
D)  4 
A)  -4 
B)  8 
C)  2 
D)  4

Question 7

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$

Accepted Answer

A)  $\frac { 5 \sqrt { 3 } } { 12 }$ 
B)  $- \frac { 5 \sqrt { 7 } } { 12 }$ 
C)  $\frac { 12 \sqrt { 3 } } { 5 }$ 
D)  $- \frac { 5 \sqrt { 3 } } { 12 }$ 
A)  $\frac { 5 \sqrt { 3 } } { 12 }$ 
B)  $- \frac { 5 \sqrt { 7 } } { 12 }$ 
C)  $\frac { 12 \sqrt { 3 } } { 5 }$ 
D)  $- \frac { 5 \sqrt { 3 } } { 12 }$

Question 8

Use the distributive property to help simplify the expression. $6 \sqrt { 45 } - 3 \sqrt { 5 }$

Accepted Answer

The answer of Use the distributive property to help simplify...

Question 9

Change the radical to simplest radical form. $\frac { \sqrt { 90 } } { \sqrt { 63 } }$

Accepted Answer

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

Question 10

Perform. $\sqrt { 3 } \sqrt [ 3 ] { 3 }$ Express answers in simplest radical form.

Accepted Answer

A)  $\sqrt [ 6 ] { 3 }$ 
B)  $\sqrt [ 5 ] { 27 }$ 
C)  $\sqrt [ 5 ] { 243 }$ 
D)  $\sqrt [ 6 ] { 243 }$ 
A)  $\sqrt [ 6 ] { 3 }$ 
B)  $\sqrt [ 5 ] { 27 }$ 
C)  $\sqrt [ 5 ] { 243 }$ 
D)  $\sqrt [ 6 ] { 243 }$

Question 11

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

Accepted Answer

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

Question 12

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 24 x ^ { 6 } y ^ { 8 } }$

Accepted Answer

A)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { 3 y }$ 
B)  $2 x ^ { 4 } y ^ { 4 } \sqrt [ 3 ] { 3 y ^ { 2 } }$ 
C)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { 3 y ^ { 2 } }$ 
D)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { y }$ 
A)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { 3 y }$ 
B)  $2 x ^ { 4 } y ^ { 4 } \sqrt [ 3 ] { 3 y ^ { 2 } }$ 
C)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { 3 y ^ { 2 } }$ 
D)  $2 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { y }$

Question 13

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { b c } ( 10 \sqrt { b c } - 7 \sqrt { b } )$

Accepted Answer

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

Question 14

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 27 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$

Accepted Answer

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

Simplify the numerical expression. 5^{- 2} + 2^{- 2}

Solve the equation. $\sqrt { 5 x + 3 } = \sqrt { 9 x - 3 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 81 x ^ { 6 } y ^ { 8 } }$

Find the indicated product. Express final results using positive integral exponents only. (3 xy ^{- 2})(8 x ^{- 3} y ⁷)

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 19 } - 9 \sqrt { 323 } ) ( 3 \sqrt { 4,913 } + \sqrt { 323 } )$

Evaluate. $\sqrt [ 6 ] { 2 ^ { 6 } }$

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$

Use the distributive property to help simplify the expression. $6 \sqrt { 45 } - 3 \sqrt { 5 }$

Change the radical to simplest radical form. $\frac { \sqrt { 90 } } { \sqrt { 63 } }$

Perform. $\sqrt { 3 } \sqrt [ 3 ] { 3 }$ Express answers in simplest radical form.

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

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 24 x ^ { 6 } y ^ { 8 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { b c } ( 10 \sqrt { b c } - 7 \sqrt { b } )$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 27 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$

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

Simplify the numerical expression. 5 - 2 + 2 - 2

Solve the equation. 5x+3=9x−3\sqrt { 5 x + 3 } = \sqrt { 9 x - 3 }5x+3​=9x−3​

Express the following expression in simplest radical form. All variables represent positive real numbers. 81x6y83\sqrt [ 3 ] { 81 x ^ { 6 } y ^ { 8 } }381x6y8​

Find the indicated product. Express final results using positive integral exponents only. (3 xy - 2)(8 x - 3 y 7)

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. (819−9323)(34,913+323)( 8 \sqrt { 19 } - 9 \sqrt { 323 } ) ( 3 \sqrt { 4,913 } + \sqrt { 323 } )(819​−9323​)(34,913​+323​)

Evaluate. 266\sqrt [ 6 ] { 2 ^ { 6 } }626​

Use the distributive property to help simplify the expression. 133−1427\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }31​3​−41​27​

Use the distributive property to help simplify the expression. 645−356 \sqrt { 45 } - 3 \sqrt { 5 }645​−35​

Change the radical to simplest radical form. 9063\frac { \sqrt { 90 } } { \sqrt { 63 } }63​90​​

Perform. 333\sqrt { 3 } \sqrt [ 3 ] { 3 }3​33​ Express answers in simplest radical form.

Solve the equation. x−13=2\sqrt [ 3 ] { x - 1 } = 23x−1​=2

Express the following expression in simplest radical form. All variables represent positive real numbers. 24x6y83\sqrt [ 3 ] { 24 x ^ { 6 } y ^ { 8 } }324x6y8​

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. bc(10bc−7b)\sqrt { b c } ( 10 \sqrt { b c } - 7 \sqrt { b } )bc​(10bc​−7b​)

Express the following expression in simplest radical form. All variables represent positive real numbers. 27xy33x2y53\frac { \sqrt [ 3 ] { 27 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }33x2y5​327xy​​

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

Simplify the numerical expression. 5^{- 2} + 2^{- 2}

Solve the equation. $\sqrt { 5 x + 3 } = \sqrt { 9 x - 3 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 81 x ^ { 6 } y ^ { 8 } }$

Find the indicated product. Express final results using positive integral exponents only. (3 xy ^{- 2})(8 x ^{- 3} y ⁷)

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $( 8 \sqrt { 19 } - 9 \sqrt { 323 } ) ( 3 \sqrt { 4,913 } + \sqrt { 323 } )$

Evaluate. $\sqrt [ 6 ] { 2 ^ { 6 } }$

Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$

Use the distributive property to help simplify the expression. $6 \sqrt { 45 } - 3 \sqrt { 5 }$

Change the radical to simplest radical form. $\frac { \sqrt { 90 } } { \sqrt { 63 } }$

Perform. $\sqrt { 3 } \sqrt [ 3 ] { 3 }$ Express answers in simplest radical form.

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

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt [ 3 ] { 24 x ^ { 6 } y ^ { 8 } }$

Find the following product and express answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { b c } ( 10 \sqrt { b c } - 7 \sqrt { b } )$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt [ 3 ] { 27 x y } } { \sqrt [ 3 ] { 3 x ^ { 2 } y ^ { 5 } } }$