Question 1

Solve the equation. $\sqrt { x ^ { 2 } + 9 } = 5$

Accepted Answer

A)  x = 4 
B)  x = 4, x = 0 
C)  x = 4, x = $-$ 4 
A)  x = 4 
B)  x = 4, x = 0 
C)  x = 4, x = $-$ 4

Question 2

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

Accepted Answer

A)  150 square yards 
B)  300 square yards 
C)  37.5 square yards 
D)  75 square yards 
A)  150 square yards 
B)  300 square yards 
C)  37.5 square yards 
D)  75 square yards

Question 3

Evaluate. $\sqrt [ 3 ] { - 8 }$

Accepted Answer

To evaluate \sqrt[3]{-8}, we are looking

Question 4

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 20 x + 12 y }$

Accepted Answer

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

Question 5

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.
-$160 \sqrt { 26 } - 2,080$

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 6

Evaluate. $- \sqrt { \frac { 81 } { 16 } }$

Accepted Answer

A)  $\frac { 9 } { 4 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $- \frac { 9 } { 4 }$ 
D)  $- \frac { 9 } { 16 }$ 
A)  $\frac { 9 } { 4 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $- \frac { 9 } { 4 }$ 
D)  $- \frac { 9 } { 16 }$

Question 7

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }$

Accepted Answer

A)  $12 \sqrt { x }$ 
B)  $14 \sqrt { 3 x }$ 
C)  $17 \sqrt { x }$ 
D)  $19 x$ 
A)  $12 \sqrt { x }$ 
B)  $14 \sqrt { 3 x }$ 
C)  $17 \sqrt { x }$ 
D)  $19 x$

Question 8

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 7 \sqrt { 64 y ^ { 3 } } - 2 \sqrt { 9 y ^ { 3 } } + 4 \sqrt { 121 y ^ { 3 } }$

Accepted Answer

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

Question 9

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 2 } + 3 \sqrt [ 3 ] { 54 } - 4 \sqrt [ 3 ] { 16 }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 2 }$ 
B)  $- 3 \sqrt [ 3 ] { 2 }$ 
C)  $3 \sqrt [ 3 ] { 3 }$ 
D)  $- 3 \sqrt [ 3 ] { 3 }$ 
A)  $3 \sqrt [ 3 ] { 2 }$ 
B)  $- 3 \sqrt [ 3 ] { 2 }$ 
C)  $3 \sqrt [ 3 ] { 3 }$ 
D)  $- 3 \sqrt [ 3 ] { 3 }$

Question 10

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $2 \sqrt { 8 x } + 8 \sqrt { 32 x } - 6 \sqrt { 50 x }$

Accepted Answer

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

Question 11

The cube root of a number can be a negative number.

Accepted Answer

A) True 
 B)False

Question 12

Change the radical to simplest radical form. $\sqrt [ 3 ] { 32 }$

Accepted Answer

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

Question 13

Extra solutions that satisfy the original equation are called extraneous solutions.

Accepted Answer

A) True 
 B)False

Question 14

Change the radical to simplest radical form. $\frac { 5 } { 8 } \sqrt { 192 }$

Accepted Answer

A)  $40 \sqrt { 3 }$ 
B)  $5 \sqrt { 3 }$ 
C)  $3 \sqrt { 5 }$ 
D)  $24 \sqrt { 5 }$ 
A)  $40 \sqrt { 3 }$ 
B)  $5 \sqrt { 3 }$ 
C)  $3 \sqrt { 5 }$ 
D)  $24 \sqrt { 5 }$

Question 15

Solve the equation. $3 \sqrt { n } = 5$

Accepted Answer

A)  $n = \frac { 5 } { 3 }$ 
B)  $n = \frac { 25 } { 9 }$ 
C)  $n = \frac { 9 } { 25 }$ 
A)  $n = \frac { 5 } { 3 }$ 
B)  $n = \frac { 25 } { 9 }$ 
C)  $n = \frac { 9 } { 25 }$

Question 16

Write $\sqrt { 8 y }$ using positive rational exponents.

Accepted Answer

A)  $8 y ^ { 2 }$ 
B)  $( 8 y ) ^ { \frac { 1 } { 2 } }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $8 y$ 
A)  $8 y ^ { 2 }$ 
B)  $( 8 y ) ^ { \frac { 1 } { 2 } }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $8 y$

Question 17

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 4 } { 5 } \sqrt { 180 x y ^ { 3 } }$

Accepted Answer

A)  $\frac { 24 x y \sqrt { 5 x y } } { 5 }$ 
B)  $\frac { 24 \sqrt { 5 x y } } { 5 }$ 
C)  $\frac { 24 y \sqrt { 5 x y } } { 5 }$ 
D)  $\frac { 24 y \sqrt { 5 x } } { 5 }$ 
A)  $\frac { 24 x y \sqrt { 5 x y } } { 5 }$ 
B)  $\frac { 24 \sqrt { 5 x y } } { 5 }$ 
C)  $\frac { 24 y \sqrt { 5 x y } } { 5 }$ 
D)  $\frac { 24 y \sqrt { 5 x } } { 5 }$

Question 18

Write $\sqrt { 2 y }$ using positive rational exponents.

Accepted Answer

The answer of Write $\sqrt { 2 y }$ using...

Question 19

Write $x ^ { \frac { 7 } { 13 } } y ^ { \frac { 1 } { 13 } }$ in radical form.

Accepted Answer

A)  $\sqrt { x ^ { 13 } y }$ 
B)  $\sqrt [ 7 ] { x ^ { 13 } y }$ 
C)  $y \sqrt [ 13 ] { x ^ { 7 } }$ 
D)  $\sqrt [ 13 ] { x ^ { 7 } y }$ 
A)  $\sqrt { x ^ { 13 } y }$ 
B)  $\sqrt [ 7 ] { x ^ { 13 } y }$ 
C)  $y \sqrt [ 13 ] { x ^ { 7 } }$ 
D)  $\sqrt [ 13 ] { x ^ { 7 } y }$

Question 20

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 1 } { 2 } \sqrt { 45 x y ^ { 3 } }$

Accepted Answer

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

Solve the equation. $\sqrt { x ^ { 2 } + 9 } = 5$

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

Evaluate. $\sqrt [ 3 ] { - 8 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 20 x + 12 y }$

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. - $160 \sqrt { 26 } - 2,080$

Evaluate. $- \sqrt { \frac { 81 } { 16 } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 7 \sqrt { 64 y ^ { 3 } } - 2 \sqrt { 9 y ^ { 3 } } + 4 \sqrt { 121 y ^ { 3 } }$

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 2 } + 3 \sqrt [ 3 ] { 54 } - 4 \sqrt [ 3 ] { 16 }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $2 \sqrt { 8 x } + 8 \sqrt { 32 x } - 6 \sqrt { 50 x }$

The cube root of a number can be a negative number.

Change the radical to simplest radical form. $\sqrt [ 3 ] { 32 }$

Extra solutions that satisfy the original equation are called extraneous solutions.

Change the radical to simplest radical form. $\frac { 5 } { 8 } \sqrt { 192 }$

Solve the equation. $3 \sqrt { n } = 5$

Write $\sqrt { 8 y }$ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 4 } { 5 } \sqrt { 180 x y ^ { 3 } }$

Write $\sqrt { 2 y }$ using positive rational exponents.

Write $x ^ { \frac { 7 } { 13 } } y ^ { \frac { 1 } { 13 } }$ in radical form.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 1 } { 2 } \sqrt { 45 x y ^ { 3 } }$

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. x2+9=5\sqrt { x ^ { 2 } + 9 } = 5x2+9​=5

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

Evaluate. −83\sqrt [ 3 ] { - 8 }3−8​

Express the following expression in simplest radical form. All variables represent positive real numbers. 20x+12y\sqrt { 20 x + 12 y }20x+12y​

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. - 16026−2,080160 \sqrt { 26 } - 2,08016026​−2,080

Evaluate. −8116- \sqrt { \frac { 81 } { 16 } }−1681​​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. −84x+216x+525x- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }−84x​+216x​+525x​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. −764y3−29y3+4121y3- 7 \sqrt { 64 y ^ { 3 } } - 2 \sqrt { 9 y ^ { 3 } } + 4 \sqrt { 121 y ^ { 3 } }−764y3​−29y3​+4121y3​

Use the distributive property to help simplify the expression. 223+3543−41632 \sqrt [ 3 ] { 2 } + 3 \sqrt [ 3 ] { 54 } - 4 \sqrt [ 3 ] { 16 }232​+3354​−4316​

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. 28x+832x−650x2 \sqrt { 8 x } + 8 \sqrt { 32 x } - 6 \sqrt { 50 x }28x​+832x​−650x​

The cube root of a number can be a negative number.

Change the radical to simplest radical form. 323\sqrt [ 3 ] { 32 }332​

Extra solutions that satisfy the original equation are called extraneous solutions.

Change the radical to simplest radical form. 58192\frac { 5 } { 8 } \sqrt { 192 }85​192​

Solve the equation. 3n=53 \sqrt { n } = 53n​=5

Write 8y\sqrt { 8 y }8y​ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. 45180xy3\frac { 4 } { 5 } \sqrt { 180 x y ^ { 3 } }54​180xy3​

Write 2y\sqrt { 2 y }2y​ using positive rational exponents.

Write x713y113x ^ { \frac { 7 } { 13 } } y ^ { \frac { 1 } { 13 } }x137​y131​ in radical form.

Express the following expression in simplest radical form. All variables represent positive real numbers. 1245xy3\frac { 1 } { 2 } \sqrt { 45 x y ^ { 3 } }21​45xy3​

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. $\sqrt { x ^ { 2 } + 9 } = 5$

Evaluate. $\sqrt [ 3 ] { - 8 }$

Express the following expression in simplest radical form. All variables represent positive real numbers. $\sqrt { 20 x + 12 y }$

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. - $160 \sqrt { 26 } - 2,080$

Evaluate. $- \sqrt { \frac { 81 } { 16 } }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 8 \sqrt { 4 x } + 2 \sqrt { 16 x } + 5 \sqrt { 25 x }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $- 7 \sqrt { 64 y ^ { 3 } } - 2 \sqrt { 9 y ^ { 3 } } + 4 \sqrt { 121 y ^ { 3 } }$

Use the distributive property to help simplify the expression. $2 \sqrt [ 3 ] { 2 } + 3 \sqrt [ 3 ] { 54 } - 4 \sqrt [ 3 ] { 16 }$

Use the distributive property to help simplify the following expression. All variables represent positive real numbers. $2 \sqrt { 8 x } + 8 \sqrt { 32 x } - 6 \sqrt { 50 x }$

Change the radical to simplest radical form. $\sqrt [ 3 ] { 32 }$

Change the radical to simplest radical form. $\frac { 5 } { 8 } \sqrt { 192 }$

Solve the equation. $3 \sqrt { n } = 5$

Write $\sqrt { 8 y }$ using positive rational exponents.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 4 } { 5 } \sqrt { 180 x y ^ { 3 } }$

Write $\sqrt { 2 y }$ using positive rational exponents.

Write $x ^ { \frac { 7 } { 13 } } y ^ { \frac { 1 } { 13 } }$ in radical form.

Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { 1 } { 2 } \sqrt { 45 x y ^ { 3 } }$