Deck 6: Radicals and Complex Numbers

Question 1

Evaluate the root without using a calculator or note that root is not a real number.

Answer 1

C

Question 2

Answer 2

B

Question 3

Find the length of the third side of the triangle by using the Pythagorean theorem.

A) 7 yards
B) 10 yards
C) 12 yards
D)

Answer 3

C

Question 4

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

Question 5

Evaluate the root without using a calculator or note that root is not a real number.

Question 6

Evaluate the root without using a calculator or note that root is not a real number.

Question 7

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

Question 8

Find the length of the third side of the triangle by using the Pythagorean theorem.

A) 10 in.
B) 12 in.
C) 14 in.
D) 28 in.

Question 9

Simplify the radical expression.

A) -5
B) 5
C) -125
D) 125

Question 10

Evaluate the root without using a calculator or note that root is not a real number.

Question 11

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

Question 12

Evaluate the root without using a calculator or note that root is not a real number.

Question 13

Evaluate the root without using a calculator or note that root is not a real number.

A) 81
B) -3
C) 3
D) Not a real number

Question 14

Evaluate the root without using a calculator or note that root is not a real number.

Question 15

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

Question 16

Question 17

Evaluate the root without using a calculator or note that root is not a real number.

Question 18

Evaluate the root without using a calculator or note that root is not a real number.

Question 19

Evaluate the root without using a calculator or note that root is not a real number.

Question 20

Evaluate the root without using a calculator or note that root is not a real number.

A) 6561
B) 9
C) -9
D) Not a real number

Question 21

Convert the expression to radical notation.

Question 22

Write the word or phrase that best completes each statement or answers the question.
Convert the expression to radical notation.

Question 23

Convert the expression to radical notation.

Question 24

Simplify the expression.

Question 25

Simplify the expression, if possible.

Question 26

Simplify the expression, if possible.

Question 27

Convert the expression to radical form and simplify.

Question 28

Write the expression by using rational exponents rather than radical notation.

Question 29

Convert the expression to radical notation.

Question 30

Simplify the expression, if possible.

Question 31

Write the domain of the function in interval notation.

Question 32

Simplify the expression, if possible.

Question 33

Write the domain of the function in interval notation.

Question 34

Simplify the expression, if possible.

Question 35

Write the word or phrase that best completes each statement or answers the question.
Evaluate the function for k (-9), k (-8), k (-7), k (-6), and k (-3). Then write the domain of the function in
interval notation.

Question 36

Convert the expression to radical form and simplify.

Question 37

Simplify the expression, if possible.

Question 38

Two mountain bikers take off from the same place at the same time. One travels north at 4 mph, and the other travels east at 3 mph. How far apart are they after 4 hr?

A) 20 mi
B) 5 mi
C) 14 mi
D) 28 mi

Question 39

Write the expression by using rational exponents rather than radical notation.

Question 40

Write the word or phrase that best completes each statement or answers the question.
How high up a vertical wall will a 26 foot long extension ladder reach if its base is placed 10 feet
away from the wall?

Question 41

Use a calculator to approximate the expression. Round to four decimal places, if necessary.

A) 108
B) 3.3019
C) 14.6969
D) 1.8171

Question 42

Write the expression using rational exponents. Then simplify and convert back to radical notation.

Question 43

Write the word or phrase that best completes each statement or answers the question.
Write the expression by using rational exponents rather than radical notation.

Question 44

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.

Question 45

Write the expression by using rational exponents rather than radical notation.

Question 46

Simplify the radical.

Question 47

Simplify the radical.

Question 48

Write the expression as a single radical.

Question 49

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.

Question 50

Simplify the radical.

Question 51

Use a calculator to approximate the expression. Round to four decimal places, if necessary.

Question 52

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.

Question 53

Write the word or phrase that best completes each statement or answers the question.
A creative group of students produces a reality television show that features various aspects of
college and dorm life. Once the show begins airing on the university's public access cable channel,
the function represents the number of weeks that pass until x percent of the
campus is watching the show. Compute w(50) to one decimal place, and interpret the result in the
context of this problem.

Question 54

Write the word or phrase that best completes each statement or answers the question.
Simplify the expression by using the properties of rational exponents. Write the final answer using positive
exponents only.

Question 55

The multiplication property of radicals indicates that if n a and n b are real numbers, then b

Question 56

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.

Question 57

Simplify the radical.

Question 58

The annual rate of return on an initial investment of P dollars is given by where A is the current value and t is the number of years since the money was invested. Find the annual rate of return on a $22,000 investment that grew to $32,000 after 10 years. Round to the
Nearest hundredth of a percent.

A) 13.82%
B) 23.82%
C) 0.04%
D) 3.82%

Question 59

Write the expression using rational exponents. Then simplify and convert back to radical notation.

Question 60

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.

Question 61

Simplify the radical.

Question 62

Add or subtract the radical expressions as indicated, if possible.

Question 63

Find the length of the third side of the triangle. Write your answer as a simplified radical.

Question 64

Simplify the radical expression.

Question 65

Simplify the radical. Assume that all variables represent positive real numbers.

Question 66

Simplify the radical. Assume that all variables represent positive real numbers.

Question 67

Add the radical expressions, if possible.

Question 68

Add or subtract the radical expressions as indicated, if possible.

Question 69

Add or subtract the radical expressions as indicated, if possible.

Question 70

Which two radicals are like?

Question 71

Which two radicals are like?

Question 72

On a certain youth league baseball diamond, the bases are 35 ft apart. Assuming home plate and the three bases form a perfect square, find the exact distance from home plate to second base. Then
Round to the nearest tenth of a foot.

Question 73

Add or subtract the radical expressions as indicated, if possible.

Question 74

Add or subtract the radical expressions as indicated, if possible.

Question 75

Simplify the radical. Assume that all variables represent positive real numbers.

Question 76

Add or subtract the radical expressions as indicated, if possible.

Question 77

Simplify the radical. Assume that all variables represent positive real numbers.

Question 78

Subtract the radical expressions, if possible.

Question 79

Simplify the radical. Assume that all variables represent positive real numbers.

Question 80

Simplify the radical.