Deck 8: Roots, Radical Expressions, and Radical Equations

Question 1

Refer to the following illustration. Find if and .

A)
B)
C)
D)
E)

Answer 1

Question 2

The size of a television screen is the diagonal measure of its rectangular screen. How large is a screen if it is 16 inches wide and 20 inches high?

A) 29 in.
B) 28 in.
C) 23 in.
D) 25 in
E) 22 in.

Answer 2

25 in

Question 3

Find the value without using a calculator.

A) -9
B) 9
C) 27
D) -27
E) not a real number

Answer 3

-9

Question 4

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

A) 5.94
B) 14.46
C) 5.94
D) 14.49
E) none of the above

Question 5

Graph the function.

A)
B)
C)
D)
E)

Question 6

Graph the function.

A)
B)
C)
D)
E)

Question 7

Find the square root without using a calculator.

A) 4
B) 6
C) 4
D) 3
E) 3

Question 8

A cubical box has a volume of 512 cubic feet. Substitute 512 for V in the formula , and solve for s to find the length of each side of the box.

A)
B) 24 cu. ft.
C) 16 cu. ft.
D) 8 cu. ft.
E) none of the above

Question 9

Is the number rational, irrational, or imaginary?

A) imaginary
B) rational
C) irrational

Question 10

Find the cube root. Give the answer to the nearest hundredth.

A) 28.09
B) 29.32
C) - 27.53
D) - 29.32
E) -28.09

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

Question 12

Is the number rational, irrational, or imaginary?

A) rational
B) irrational
C) imaginary

Question 13

Graph the function.

A)
B)
C)
D)
E)

Question 14

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.

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

Question 15

Graph the function.

A)
B)
C)
D)
E)

Question 16

Find the cube root. Give the answer to the nearest hundredth.

A) -0.48
B) 0.42
C) 0.48
D) -0.42
E) -0.44

Question 17

Find the square root without using a calculator.

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

Question 18

Find the area of the isosceles triangle shown in the illustration, where a = 11 and b = 10.

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

Question 19

Is the number rational, irrational, or imaginary?

A) irrational
B) imaginary
C) rational

Question 20

Find the value without using a calculator.

A) 9
B) 0.1
C) 10
D) 0.3
E) 1

Question 21

Use the distributive property to help simplify the expression.

A)
B)
C)
D)
E)

Question 22

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

A) 6.62
B) 23.36
C) 10.63

Question 23

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

A)
B)
C)
D)
E)

Question 24

Find the value.

A) -9
B) 9
C)
D) - 1
E) 1

Question 25

Use the distributive property to help simplify the expression.

A)
B)
C)
D)
E)

Question 26

Simplify the expression.

A)
B)
C)
D)
E)

Question 27

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

A)
B)
C)
D)
E)

Question 28

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

A)
B)
C)
D)
E)

Question 29

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

A)
B)
C)
D)
E)

Question 30

Use the distributive property to help simplify the expression.

A)
B)
C)
D)
E)

Question 31

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

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

Question 32

Use the distributive property to help simplify the expression.

A)
B)
C)
D)
E)

Question 33

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

A)
B)
C)
D)
E)

Question 34

Simplify the expression.

A)
B)
C)
D)
E)

Question 35

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

A)
B)
C)
D)
E)

Question 36

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

A)
B)
C)
D)
E)

Question 37

Find the value.

Question 38

This graph is

A)
B)
C)
D)

Question 39

Simplify the expression.

A)
B)
C)
D)
E)

Question 40

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

A)
B)
C)
D)
E)

Question 41

Find the following product and express your answer in simplest radical form.

A)
B)
C)
D)
E)

Question 42

Solve the equation. Check all solutions.

A) 86
B) 111
C) 88
D) 77
E) no solution

Question 43

Simplify the expression.

A)
B)
C)
D)
E)

Question 44

Simplify the expression.

A)
B)
C)
D)
E)

Question 45

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

A)
B)
C)
D)
E)

Question 46

Solve the equation. Check all solutions.

A) 17
B) 16
C) 4
D) 19
E) no solution

Question 47

Perform the division by rationalizing the denominator and simplifying.

A)
B)
C)
D)
E)

Question 48

Solve the equation.

A) x = 121
B) x = 8
C) x = 64
D) x = 11
E) no solution

Question 49

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

A)
B)
C)
D)

Question 50

Rationalize the denominator and simplify.

A)
B)
C)
D)
E)

Question 51

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

A)
B)
C)
D)
E)

Question 52

Solve the equation. Check all solutions.

A) 81
B) 41
C) 9
D) 79
E) no solution

Question 53

Solve the equation.

A) 0
B) 3
C) -3
D) -3, 3
E) no solution

Question 54

Find the following product and express your answer in simplest radical form.

A)
B)
C)
D)
E)

Question 55

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

A)
B)
C)
D)
E)

Question 56

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

A)
B)
C)
D)
E)

Question 57

Perform the division by rationalizing the denominator and simplifying.

A)
B)
C)
D)
E)

Question 58

Solve the equation.

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

Question 59

Multiply and simplify where possible.

A)
B)
C)
D)
E)

Question 60

Multiply and simplify where possible.

A)
B)
C)
D)
E)

Question 61

Evaluate the expression.

A)
B)
C)
D)
E) not real

Question 62

Solve the equation. Check all solutions.

A) 51
B) 102
C) 4
D) 54
E) no solution

Question 63

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

A)
B)
C)
D)
E)

Question 64

Simplify:

A)
B)
C) not a real number
D)

Question 65

The formula relates the speed (in mph) of a car and the distance of the skid when a driver hits the brakes. On wet pavement, . How far will a car skid if it is going 50 mph?

A) about 215 ft
B) about 272 ft
C) about 238 ft
D) about 193 ft
E) about 226 ft

Question 66

Find the distance between points P and Q , where P (2, 6) and Q (-1, -10).

A)
B)
C)
D)
E)

Question 67

Evaluate the expression.

A)
B)
C)
D)
E)

Question 68

Simplify the expression.

A)
B)
C)
D)
E)

Question 69

Simplify the expression.

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

Question 70

Simplify:

A) 2
B) 74
C) 8
D) 28

Question 71

Evaluate the expression.

A)
B)
C)
D)
E) not real

Question 72

Solve the equation. Check all solutions.

A) 125
B) 250
C) 5
D) 123
E) no solution

Question 73

Find the distance between the two points. (11, 14) and (-4, -4)

A)
B)
C) 61
D)
E)

Question 74

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

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

Question 75

The orbital speed ( s ) of an earth satellite is related to its distance ( r ) from the earth's center by the formula . If the satellite's orbital speed is meters per second, find its altitude a (in meters) above the earth's surface, as shown in the illustration. Round the answer to the nearest meter.

A) 3,173
B) 11,186
C) 10,073,164
D) 10,078,964
E) 10,067,364

Question 76

The number of wrenches that can be produced at a given price can be predicted by the formula , where is the supply (in thousands) and is the price (in dollars). If the demand for the wrenches can be predicted by the formula , find the equilibrium price.

A) $5
B) $4
C) $3
D) None of the above

Question 77

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

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

Question 78

Simplify the expression.

A)
B)
C)
D)
E)