Question 1

Simplify the expression. Assume that all variables represent positive numbers.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    C

Question 2

Express the following expression in simplest radical form. All variables represent positive real numbers.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 3

Rationalize the denominator and simplify. The variable represents a positive real number.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 4

Solve the equation.

Accepted Answer

A)  t = 5 
B)  t = 3 
C)  t = 4 
D)  t = 4, 5 
E)  no solution 
A)  t = 5 
B)  t = 3 
C)  t = 4 
D)  t = 4, 5 
E)  no solution

Question 5

Simplify the expression.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Use a calculator to find the root to the nearest hundredth.

Accepted Answer

A)  6.62 
B)  23.36 
C)  10.63 
A)  6.62 
B)  23.36 
C)  10.63

Question 7

Find the square root without using a calculator.

Accepted Answer

A)  0.3 
B)  2 
C)  0.02 
D)  0.1 
E)  0.2 
A)  0.3 
B)  2 
C)  0.02 
D)  0.1 
E)  0.2

Question 8

Simplify the expression. Assume that all variables represent positive numbers.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Use the distributive property to help simplify the expression.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Perform the division by rationalizing the denominator and simplifying.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

The design for a set of brass pipes for a church organ are shown in the illustration below, where the red line is the graph of function .     Find the length of each pipe (to the nearest tenth of a foot), and then find the total length of pipe needed to construct this set (to the nearest tenth of a foot). __________ ft

Accepted Answer

The answer of The design for a set of brass...

Question 12

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous.

Accepted Answer

A)    is extraneous 
B)    is extraneous 
C)    
D)    
E)    
A)    is extraneous 
B)    is extraneous 
C)    
D)    
E)

Question 13

Write the quotient as the quotient of two radicals and simplify.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Use the distributive property to help simplify the expression.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the distance between two points. (-1, 4) and (5, 12)

Accepted Answer

A)  10 
B)  15 
C)  13 
D)  7 
E)  8 
A)  10 
B)  15 
C)  13 
D)  7 
E)  8

Question 16

Perform the operation. Do not use negative exponents in the answer.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Simplify the expression.

Accepted Answer

A)  49 
B)    
C)  6 
D)  36 
E)  81 
A)  49 
B)    
C)  6 
D)  36 
E)  81

Question 18

A team of archaeologists travels 3.6 miles east and then 2.8 miles north of their base camp to explore some ancient ruins. "As the crow flies", how far from their base camp are they? Round to the nearest whole number.

Accepted Answer

A)  6 mi 
B)  7 mi 
C)  15 mi 
D)  5 mi 
E)  4 mi 
A)  6 mi 
B)  7 mi 
C)  15 mi 
D)  5 mi 
E)  4 mi

Question 19

Express the following radical in simplest radical form. All variables represent nonnegative real numbers.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Write the quotient as the quotient of two radicals and simplify.

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Simplify the expression. Assume that all variables represent positive numbers.

Express the following expression in simplest radical form. All variables represent positive real numbers.

Rationalize the denominator and simplify. The variable represents a positive real number.

Solve the equation.

Simplify the expression.

Use a calculator to find the root to the nearest hundredth.

Find the square root without using a calculator.

Simplify the expression. Assume that all variables represent positive numbers.

Use the distributive property to help simplify the expression.

Perform the division by rationalizing the denominator and simplifying.

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous.

Write the quotient as the quotient of two radicals and simplify.

Use the distributive property to help simplify the expression.

Find the distance between two points. (-1, 4) and (5, 12)

Perform the operation. Do not use negative exponents in the answer.

Simplify the expression.

A team of archaeologists travels 3.6 miles east and then 2.8 miles north of their base camp to explore some ancient ruins. "As the crow flies", how far from their base camp are they? Round to the nearest whole number.

Express the following radical in simplest radical form. All variables represent nonnegative real numbers.

Write the quotient as the quotient of two radicals and simplify.

Real Numbers and Their Basic Properties

Equations and Inequalities

Graphs; Equations of Lines; Functions; Variation

Polynomials

Factoring Polynomials and Solving Equations by Factoring

Rational Expressions and Equations; Ratio and Proportion

Systems of Linear Equations and Inequalities in Two Variables

Quadratic Equations, Quadratic Functions, and Complex Numbers

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Exam 8: Roots, Radical Expressions, and Radical Equations

Simplify the expression. Assume that all variables represent positive numbers.

Express the following expression in simplest radical form. All variables represent positive real numbers.

Rationalize the denominator and simplify. The variable represents a positive real number.

Solve the equation.

Simplify the expression.

Use a calculator to find the root to the nearest hundredth.

Find the square root without using a calculator.

Simplify the expression. Assume that all variables represent positive numbers.

Use the distributive property to help simplify the expression.

Perform the division by rationalizing the denominator and simplifying.

Solve the equation. Write all solutions and then indicate which of those solutions are extraneous.

Write the quotient as the quotient of two radicals and simplify.

Use the distributive property to help simplify the expression.

Find the distance between two points. (-1, 4) and (5, 12)

Perform the operation. Do not use negative exponents in the answer.

Simplify the expression.

A team of archaeologists travels 3.6 miles east and then 2.8 miles north of their base camp to explore some ancient ruins. "As the crow flies", how far from their base camp are they? Round to the nearest whole number.

Express the following radical in simplest radical form. All variables represent nonnegative real numbers.

Write the quotient as the quotient of two radicals and simplify.

Real Numbers and Their Basic Properties

Equations and Inequalities

Graphs; Equations of Lines; Functions; Variation

Polynomials

Factoring Polynomials and Solving Equations by Factoring

Rational Expressions and Equations; Ratio and Proportion

Systems of Linear Equations and Inequalities in Two Variables

Quadratic Equations, Quadratic Functions, and Complex Numbers

Filters