Question 1

Solve the equation. $\sqrt { n - 7 } + \sqrt { n + 9 } = 2 \sqrt { n }$

Accepted Answer

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

Question 2

To multiply radicals, multiply the indices and multiply the radicands, simplify if necessary.

Accepted Answer

A) True 
 B)False

Question 3

Solve the equation. $\sqrt { 3 y + 43 } = 7$

Accepted Answer

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

Question 4

Evaluate the numerical expression. $81 ^ { \frac { 1 } { 2 } }$

Accepted Answer

A)  9 
B)  $\frac { 1 } { 9 }$ 
C)  40.5 
D)  6,561 
A)  9 
B)  $\frac { 1 } { 9 }$ 
C)  40.5 
D)  6,561

Question 5

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 45 x }$

Accepted Answer

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

Question 6

Solve the equation. $2 \sqrt { n } - 3 = 0$

Accepted Answer

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

Question 7

Use the distributive property to help simplify the expression. $9 \sqrt { 125 } - 2 \sqrt { 5 } - 2 \sqrt { 20 }$

Accepted Answer

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

Question 8

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement.
-$64 a \sqrt { d } + 64 a$

Accepted Answer

A)  $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$ 
B)  $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$ 
C)  $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$ 
D)  $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$ 
A)  $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$ 
B)  $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$ 
C)  $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$ 
D)  $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$

Question 9

The square root of x squared is the absolute value of x .

Accepted Answer

A) True 
 B)False

Question 10

Write $( 5.26 ) ( 10 ) ^ { - 2 }$ in ordinary decimal notation.

Accepted Answer

A)  0.0521 
B)  0.526 
C)  0.00526 
D)  0.0531 
E)  0.0526 
A)  0.0521 
B)  0.526 
C)  0.00526 
D)  0.0531 
E)  0.0526

Question 11

Solve each equation. Match each equation with the corresponding solution.
-$n = \frac { 36 } { 121 }$

Accepted Answer

A)  $6 \sqrt { n } = 11$ 
B)  $11 \sqrt { n } = 6$ 
A)  $6 \sqrt { n } = 11$ 
B)  $11 \sqrt { n } = 6$

Question 12

When an expression with a rational exponent is written as a radical express, the numerator of the rational exponent is the index of the radical

Accepted Answer

A) True 
 B)False

Question 13

Write $18 x ^ { \frac { 8 } { 5 } }$ in radical form.

Accepted Answer

The answer of Write \(18 x ^ { \frac {...

Question 14

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement.
-$16 \sqrt { 38 } - 8 \sqrt { 323 }$

Accepted Answer

A)  $8 \sqrt { 19 } ( 2 \sqrt { 2 } - \sqrt { 17 } )$ 
B)  $10 \sqrt { 13 } ( 2 \sqrt { 19 } - 8 \sqrt { 17 } )$ 
C)  $10 \sqrt { 26 } ( 8 \sqrt { 8 } - 19 \sqrt { 52 } )$ 
D)  $- 4 \sqrt { 19 } ( 10 \sqrt { 19 } + 4 \sqrt { 52 } )$ 
E)  $- 10 \sqrt { 13 } ( 8 \sqrt { 52 } - 8 \sqrt { 8 } )$ 
A)  $8 \sqrt { 19 } ( 2 \sqrt { 2 } - \sqrt { 17 } )$ 
B)  $10 \sqrt { 13 } ( 2 \sqrt { 19 } - 8 \sqrt { 17 } )$ 
C)  $10 \sqrt { 26 } ( 8 \sqrt { 8 } - 19 \sqrt { 52 } )$ 
D)  $- 4 \sqrt { 19 } ( 10 \sqrt { 19 } + 4 \sqrt { 52 } )$ 
E)  $- 10 \sqrt { 13 } ( 8 \sqrt { 52 } - 8 \sqrt { 8 } )$

Question 15

Simplify the numerical expression. $\left( \frac { 2 ^ { - 1 } } { 7 ^ { - 2 } } \right) ^ { - 1 }$ Please enter your answer as a fraction.

Accepted Answer

The answer of Simplify the numerical expression. \(\left( \frac {...

Question 16

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { c } } { \sqrt { c } - 8 }$ Please enter your answer as a fraction.

Accepted Answer

The answer of Rationalize the denominator and simplify. All variables...

Question 17

Write $- \sqrt [ 4 ] { x + y }$ using positive rational exponents.

Accepted Answer

The answer of Write \(- \sqrt [ 4 ] {...

Question 18

Solve the equation. $\sqrt { x + 8 } = \sqrt { x - 1 } + 1$

Accepted Answer

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

Question 19

Write $x ^ { \frac { 3 } { 8 } }$ in radical form.

Accepted Answer

A)  $\sqrt { x ^ { 3 } }$ 
B)  $\sqrt [ 3 ] { x ^ { 8 } }$ 
C)  $\sqrt [ 8 ] { x ^ { 3 } }$ 
D)  $\sqrt { x ^ { 8 } }$ 
A)  $\sqrt { x ^ { 3 } }$ 
B)  $\sqrt [ 3 ] { x ^ { 8 } }$ 
C)  $\sqrt [ 8 ] { x ^ { 3 } }$ 
D)  $\sqrt { x ^ { 8 } }$

Question 20

Evaluate the numerical expression. $\left( \frac { 1 } { 125 } \right) ^ { - \frac { 1 } { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 125 }$ 
B)  375 
C)  $\frac { 1 } { 5 }$ 
D)  5 
A)  $\frac { 1 } { 125 }$ 
B)  375 
C)  $\frac { 1 } { 5 }$ 
D)  5

Solve the equation. $\sqrt { n - 7 } + \sqrt { n + 9 } = 2 \sqrt { n }$

To multiply radicals, multiply the indices and multiply the radicands, simplify if necessary.

Solve the equation. $\sqrt { 3 y + 43 } = 7$

Evaluate the numerical expression. $81 ^ { \frac { 1 } { 2 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 45 x }$

Solve the equation. $2 \sqrt { n } - 3 = 0$

Use the distributive property to help simplify the expression. $9 \sqrt { 125 } - 2 \sqrt { 5 } - 2 \sqrt { 20 }$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $64 a \sqrt { d } + 64 a$

The square root of x squared is the absolute value of x .

Write $( 5.26 ) ( 10 ) ^ { - 2 }$ in ordinary decimal notation.

Solve each equation. Match each equation with the corresponding solution. - $n = \frac { 36 } { 121 }$

When an expression with a rational exponent is written as a radical express, the numerator of the rational exponent is the index of the radical

Write $18 x ^ { \frac { 8 } { 5 } }$ in radical form.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $16 \sqrt { 38 } - 8 \sqrt { 323 }$

Simplify the numerical expression. $\left( \frac { 2 ^ { - 1 } } { 7 ^ { - 2 } } \right) ^ { - 1 }$ Please enter your answer as a fraction.

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { c } } { \sqrt { c } - 8 }$ Please enter your answer as a fraction.

Write $- \sqrt [ 4 ] { x + y }$ using positive rational exponents.

Solve the equation. $\sqrt { x + 8 } = \sqrt { x - 1 } + 1$

Write $x ^ { \frac { 3 } { 8 } }$ in radical form.

Evaluate the numerical expression. $\left( \frac { 1 } { 125 } \right) ^ { - \frac { 1 } { 3 } }$

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. n−7+n+9=2n\sqrt { n - 7 } + \sqrt { n + 9 } = 2 \sqrt { n }n−7​+n+9​=2n​

To multiply radicals, multiply the indices and multiply the radicands, simplify if necessary.

Solve the equation. 3y+43=7\sqrt { 3 y + 43 } = 73y+43​=7

Evaluate the numerical expression. 811281 ^ { \frac { 1 } { 2 } }8121​

Express the following expression in simplest radical form. All variables represent positive real numbers. 45x\sqrt { 45 x }45x​

Solve the equation. 2n−3=02 \sqrt { n } - 3 = 02n​−3=0

Use the distributive property to help simplify the expression. 9125−25−2209 \sqrt { 125 } - 2 \sqrt { 5 } - 2 \sqrt { 20 }9125​−25​−220​

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - 64ad+64a64 a \sqrt { d } + 64 a64ad​+64a

The square root of x squared is the absolute value of x .

Write (5.26)(10)−2( 5.26 ) ( 10 ) ^ { - 2 }(5.26)(10)−2 in ordinary decimal notation.

Solve each equation. Match each equation with the corresponding solution. - n=36121n = \frac { 36 } { 121 }n=12136​

When an expression with a rational exponent is written as a radical express, the numerator of the rational exponent is the index of the radical

Write 18x8518 x ^ { \frac { 8 } { 5 } }18x58​ in radical form.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - 1638−832316 \sqrt { 38 } - 8 \sqrt { 323 }1638​−8323​

Simplify the numerical expression. (2−17−2)−1\left( \frac { 2 ^ { - 1 } } { 7 ^ { - 2 } } \right) ^ { - 1 }(7−22−1​)−1 Please enter your answer as a fraction.

Rationalize the denominator and simplify. All variables represent positive real numbers. cc−8\frac { \sqrt { c } } { \sqrt { c } - 8 }c​−8c​​ Please enter your answer as a fraction.

Write −x+y4- \sqrt [ 4 ] { x + y }−4x+y​ using positive rational exponents.

Solve the equation. x+8=x−1+1\sqrt { x + 8 } = \sqrt { x - 1 } + 1x+8​=x−1​+1

Write x38x ^ { \frac { 3 } { 8 } }x83​ in radical form.

Evaluate the numerical expression. (1125)−13\left( \frac { 1 } { 125 } \right) ^ { - \frac { 1 } { 3 } }(1251​)−31​

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. $\sqrt { n - 7 } + \sqrt { n + 9 } = 2 \sqrt { n }$

Solve the equation. $\sqrt { 3 y + 43 } = 7$

Evaluate the numerical expression. $81 ^ { \frac { 1 } { 2 } }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 45 x }$

Solve the equation. $2 \sqrt { n } - 3 = 0$

Use the distributive property to help simplify the expression. $9 \sqrt { 125 } - 2 \sqrt { 5 } - 2 \sqrt { 20 }$

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $64 a \sqrt { d } + 64 a$

Write $( 5.26 ) ( 10 ) ^ { - 2 }$ in ordinary decimal notation.

Solve each equation. Match each equation with the corresponding solution. - $n = \frac { 36 } { 121 }$

Write $18 x ^ { \frac { 8 } { 5 } }$ in radical form.

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement. - $16 \sqrt { 38 } - 8 \sqrt { 323 }$

Simplify the numerical expression. $\left( \frac { 2 ^ { - 1 } } { 7 ^ { - 2 } } \right) ^ { - 1 }$ Please enter your answer as a fraction.

Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { c } } { \sqrt { c } - 8 }$ Please enter your answer as a fraction.

Write $- \sqrt [ 4 ] { x + y }$ using positive rational exponents.

Solve the equation. $\sqrt { x + 8 } = \sqrt { x - 1 } + 1$

Write $x ^ { \frac { 3 } { 8 } }$ in radical form.

Evaluate the numerical expression. $\left( \frac { 1 } { 125 } \right) ^ { - \frac { 1 } { 3 } }$