Question 1

Solve the equation. $\sqrt { x ^ { 2 } + 5 x + 7 } = 1$

Accepted Answer

A)  x = 3, x = 2 
B)  x = 3, x = $-$ 2. 
C)  x = 3, x = $-$ 2 
A)  x = 3, x = 2 
B)  x = 3, x = $-$ 2. 
C)  x = 3, x = $-$ 2

Question 2

Evaluate. $- \sqrt { \frac { 49 } { 4 } }$

Accepted Answer

The answer of Evaluate. \(- \sqrt { \frac { 49...

Question 3

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 7 x } { 6 y } }$

Accepted Answer

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

Question 4

Write $6 x ^ { \frac { 8 } { 7 } }$ in radical form.

Accepted Answer

A)  $6 \sqrt [ 8 ] { x ^ { 7 } }$ 
B)  $\sqrt [ 7 ] { 6 x ^ { 8 } }$ 
C)  $6 \sqrt [ 7 ] { x ^ { 8 } }$ 
D)  $\sqrt { x ^ { 7 } }$ 
A)  $6 \sqrt [ 8 ] { x ^ { 7 } }$ 
B)  $\sqrt [ 7 ] { 6 x ^ { 8 } }$ 
C)  $6 \sqrt [ 7 ] { x ^ { 8 } }$ 
D)  $\sqrt { x ^ { 7 } }$

Question 5

Solve the equation. $\sqrt { - 3 x + 13 } = x - 3$

Accepted Answer

The answer of Solve the equation. \(\sqrt { - 3...

Question 6

Change the radical to simplest radical form. $- \frac { 3 } { 16 } \sqrt { 20 }$

Accepted Answer

A)  $- \frac { \sqrt { 5 } } { 8 }$ 
B)  $- 3 \sqrt { 5 }$ 
C)  $3 \sqrt { 5 }$ 
D)  $- \frac { 3 \sqrt { 5 } } { 8 }$ 
A)  $- \frac { \sqrt { 5 } } { 8 }$ 
B)  $- 3 \sqrt { 5 }$ 
C)  $3 \sqrt { 5 }$ 
D)  $- \frac { 3 \sqrt { 5 } } { 8 }$

Question 7

The numerator of the rational exponent for cube root is 3.

Accepted Answer

A) True 
 B)False

Question 8

Simplify. Express final results using positive exponents only. $\left( \frac { x ^ { 5 } } { y ^ { 6 } } \right) ^ { - \frac { 1 } { 5 } }$

Accepted Answer

A)  $\frac { y ^ { 6 } } { x }$ 
B)  $\frac { y ^ { \frac { 6 } { 5 } } } { x }$ 
C)  $\frac { x ^ { \frac { 6 } { 5 } } } { y }$ 
D)  $\frac { y ^ { \frac { 5 } { 6 } } } { x }$ 
A)  $\frac { y ^ { 6 } } { x }$ 
B)  $\frac { y ^ { \frac { 6 } { 5 } } } { x }$ 
C)  $\frac { x ^ { \frac { 6 } { 5 } } } { y }$ 
D)  $\frac { y ^ { \frac { 5 } { 6 } } } { x }$

Question 9

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 11 x } { 2 y } }$

Accepted Answer

A)  $\frac { \sqrt { 11 x y } } { \sqrt { 2 y } }$ 
B)  $\frac { \sqrt { 22 x y } } { 2 }$ 
C)  $\frac { \sqrt { 11 x y } } { 2 y }$ 
D)  $\frac { \sqrt { 22 x y } } { 2 y }$ 
A)  $\frac { \sqrt { 11 x y } } { \sqrt { 2 y } }$ 
B)  $\frac { \sqrt { 22 x y } } { 2 }$ 
C)  $\frac { \sqrt { 11 x y } } { 2 y }$ 
D)  $\frac { \sqrt { 22 x y } } { 2 y }$

Question 10

Simplify the numerical expression. 2 - 4

Accepted Answer

A)  $16$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 1 } { 16 }$ 
A)  $16$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 1 } { 16 }$

Question 11

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

Accepted Answer

A)  $64$ 
B)  $27$ 
C)  $\frac { 1 } { 27 }$ 
A)  $64$ 
B)  $27$ 
C)  $\frac { 1 } { 27 }$

Question 12

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

Accepted Answer

The answer of Solve the equation. \(\sqrt { 2 x...

Question 13

Solve the equation. $\sqrt { x ^ { 2 } - x + 16 } = x + 4$

Accepted Answer

The answer of Solve the equation. \(\sqrt { x ^...

Question 14

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 21 } } { \sqrt [ 3 ] { 7 } }$

Accepted Answer

A)  $\sqrt [ 3 ] { 3 }$ 
B)  3 
C)  $\sqrt [ 3 ] { 14 }$ 
D)  $7 \sqrt [ 3 ] { 21 }$ 
A)  $\sqrt [ 3 ] { 3 }$ 
B)  3 
C)  $\sqrt [ 3 ] { 14 }$ 
D)  $7 \sqrt [ 3 ] { 21 }$

Question 15

Write 70,000,000 in scientific notation.

Accepted Answer

The answer of Write 70,000,000 in scientific notation....

Question 16

Write $x ^ { \frac { 5 } { 8 } } y ^ { \frac { 1 } { 8 } }$ in radical form.

Accepted Answer

The answer of Write \(x ^ { \frac { 5...

Question 17

The number under the radical sign is called the radical.

Accepted Answer

A) True 
 B)False

Question 18

Change the radical to simplest radical form. $\sqrt { \frac { 19 } { 64 } }$

Accepted Answer

A)  $19 \sqrt { 8 }$ 
B)  $8 \sqrt { 19 }$ 
C)  $\frac { \sqrt { 19 } } { 8 }$ 
D)  $\frac { \sqrt { 8 } } { 19 }$ 
A)  $19 \sqrt { 8 }$ 
B)  $8 \sqrt { 19 }$ 
C)  $\frac { \sqrt { 19 } } { 8 }$ 
D)  $\frac { \sqrt { 8 } } { 19 }$

Question 19

Solve the equation. $7 \sqrt { x } + 8 = x$

Accepted Answer

A)  x = 64, x = -64 
B)  x = 64 
C)  x = 64, x = 1 
A)  x = 64, x = -64 
B)  x = 64 
C)  x = 64, x = 1

Question 20

Simplify the numerical expression. $-$ 10 - 4

Accepted Answer

A)  $- \frac { 1 } { 1,000 }$ 
B)  $- \frac { 1 } { 10,000 }$ 
C)  $- 10,000$ 
A)  $- \frac { 1 } { 1,000 }$ 
B)  $- \frac { 1 } { 10,000 }$ 
C)  $- 10,000$

Solve the equation. $\sqrt { x ^ { 2 } + 5 x + 7 } = 1$

Evaluate. $- \sqrt { \frac { 49 } { 4 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 7 x } { 6 y } }$

Write $6 x ^ { \frac { 8 } { 7 } }$ in radical form.

Solve the equation. $\sqrt { - 3 x + 13 } = x - 3$

Change the radical to simplest radical form. $- \frac { 3 } { 16 } \sqrt { 20 }$

The numerator of the rational exponent for cube root is 3.

Simplify. Express final results using positive exponents only. $\left( \frac { x ^ { 5 } } { y ^ { 6 } } \right) ^ { - \frac { 1 } { 5 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 11 x } { 2 y } }$

Simplify the numerical expression. 2^{- 4}

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

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

Solve the equation. $\sqrt { x ^ { 2 } - x + 16 } = x + 4$

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 21 } } { \sqrt [ 3 ] { 7 } }$

Write 70,000,000 in scientific notation.

Write $x ^ { \frac { 5 } { 8 } } y ^ { \frac { 1 } { 8 } }$ in radical form.

The number under the radical sign is called the radical.

Change the radical to simplest radical form. $\sqrt { \frac { 19 } { 64 } }$

Solve the equation. $7 \sqrt { x } + 8 = x$

Simplify the numerical expression. $-$ 10 - 4

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

Solve the equation. x2+5x+7=1\sqrt { x ^ { 2 } + 5 x + 7 } = 1x2+5x+7​=1

Evaluate. −494- \sqrt { \frac { 49 } { 4 } }−449​​

Express the following expression in simplest radical form. All variables represent positive real numbers. 7x6y\sqrt { \frac { 7 x } { 6 y } }6y7x​​

Write 6x876 x ^ { \frac { 8 } { 7 } }6x78​ in radical form.

Solve the equation. −3x+13=x−3\sqrt { - 3 x + 13 } = x - 3−3x+13​=x−3

Change the radical to simplest radical form. −31620- \frac { 3 } { 16 } \sqrt { 20 }−163​20​

The numerator of the rational exponent for cube root is 3.

Simplify. Express final results using positive exponents only. (x5y6)−15\left( \frac { x ^ { 5 } } { y ^ { 6 } } \right) ^ { - \frac { 1 } { 5 } }(y6x5​)−51​

Express the following expression in simplest radical form. All variables represent positive real numbers. 11x2y\sqrt { \frac { 11 x } { 2 y } }2y11x​​

Simplify the numerical expression. 2 - 4

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

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

Solve the equation. x2−x+16=x+4\sqrt { x ^ { 2 } - x + 16 } = x + 4x2−x+16​=x+4

Change the radical to simplest radical form. 21373\frac { \sqrt [ 3 ] { 21 } } { \sqrt [ 3 ] { 7 } }37​321​​

Write 70,000,000 in scientific notation.

Write x58y18x ^ { \frac { 5 } { 8 } } y ^ { \frac { 1 } { 8 } }x85​y81​ in radical form.

The number under the radical sign is called the radical.

Change the radical to simplest radical form. 1964\sqrt { \frac { 19 } { 64 } }6419​​

Solve the equation. 7x+8=x7 \sqrt { x } + 8 = x7x​+8=x

Simplify the numerical expression. −-− 10 - 4

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

Solve the equation. $\sqrt { x ^ { 2 } + 5 x + 7 } = 1$

Evaluate. $- \sqrt { \frac { 49 } { 4 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 7 x } { 6 y } }$

Write $6 x ^ { \frac { 8 } { 7 } }$ in radical form.

Solve the equation. $\sqrt { - 3 x + 13 } = x - 3$

Change the radical to simplest radical form. $- \frac { 3 } { 16 } \sqrt { 20 }$

Simplify. Express final results using positive exponents only. $\left( \frac { x ^ { 5 } } { y ^ { 6 } } \right) ^ { - \frac { 1 } { 5 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { \frac { 11 x } { 2 y } }$

Simplify the numerical expression. 2^{- 4}

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

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

Solve the equation. $\sqrt { x ^ { 2 } - x + 16 } = x + 4$

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 21 } } { \sqrt [ 3 ] { 7 } }$

Write $x ^ { \frac { 5 } { 8 } } y ^ { \frac { 1 } { 8 } }$ in radical form.

Change the radical to simplest radical form. $\sqrt { \frac { 19 } { 64 } }$

Solve the equation. $7 \sqrt { x } + 8 = x$

Simplify the numerical expression. $-$ 10 - 4