Deck 8: Roots and Radicals

Question 1

Find x in the right triangle.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the root.

A)
B)
C)
D)
E)

Answer 2

Question 3

The higher you are above the ground, the farther you can see. If your view is unobstructed, then the distance in miles that you can see from h feet above the ground is given by the formula The following figure shows a lighthouse with a door and windows at various heights. The preceding formula can be used to find the distance to the ocean horizon from these heights. Use the formula and a calculator to complete the following table. Round your answers to the nearest whole number.

A)
B)
C)
D)

Answer 3

Question 4

Find the root.

A)
B)
C)
D)
E)

Question 5

Assume the variable is positive, and find the root.

A)
B)
C)
D)
E)

Question 6

Simplify the expression.

A)32
B)34
C)4
D)2
E)

Question 7

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 15 feet higher than the right bank and the stream is 20 feet wide, how long must a log be to just barely reach? __________ feet

Question 8

Find the root.

A)
B)
C)
D)
E)

Question 9

Simplify the pair of expressions.

A)
B)
C)
D)
E)

Question 10

Assume all variables are positive, and find the root.

A)
B)
C)
D)
E)

Question 11

Assume the variable is positive, and find the root.

A)
B)
C)
D)
E)

Question 12

Find the root.

A)
B)
C)
D)
E)

Question 13

Simplify the expression.

A)
B)
C)
D)
E)

Question 14

Assume all variables are positive, and find the root.

A)
B)
C)
D)
E)

Question 15

Find the root.

A)
B)
C)
D)
E)

Question 16

Assume the variable is positive, and find the root.

A)
B)
C)
D)
E)

Question 17

Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 7 feet higher than the right bank and the stream is 24 feet wide, how long must a log be to just barely reach?

A)
B)
C)
D)
E)

Question 18

Find the root.

A)
B)
C)
D)
E)

Question 19

Assume the variable and use the fact that to find .

A)
B)
C)
D)
E)

Question 20

Assume the variable is positive, and find the root.

A)
B)
C)
D)
E)

Question 21

Use a calculator to help complete the table. If an answer needs rounding, round to the nearest thousandth.

A)
B)
C)
D)

Question 22

Simplify the expression.

Question 23

Find the root. If the root does not exist as a real number, write not a real number .

Question 24

Find x in the right triangle.

Question 25

Simplify the expression.

Question 26

Assume all variables are positive, and find the root.

Question 27

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

A)
B)
C)
D)
E)

Question 28

Find the root.

Question 29

Assume the variable and use the fact that to find .

Question 30

Find the root.

Question 31

Assume the variable is positive, and find the root.

Question 32

Find the root.

Question 33

Assume all variables are positive, and find the root.

Question 34

Use property 2 of the radicals to simplify the following. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 35

Find the root. If the root does not exist as a real number, write not a real number .

Question 36

Assume the variable is positive, and find the root.

Question 37

Assume the variable is positive, and find the root.

Question 38

Simplify the pair of expressions. = __________ = __________

Question 39

Assume the variable is positive, and find the root.

Question 40

Find the root.

Question 41

Simplify the radical expression as much as possible.

Question 42

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

Question 43

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 44

Simplify the radical expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 45

Simplify the radical expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 46

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

A)
B)
C)
D)
E)

Question 47

Use property 2 of the radicals to simplify the following.

A)
B)
C)
D)
E)

Question 48

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

Question 49

Use property 2 of the radicals to simplify the following. Assume all variables represent positive numbers.

Question 50

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 51

Simplify the radical expression as much as possible.

A)
B)
C)
D)
E)

Question 52

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 53

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

A)
B)
C)
D)
E)

Question 54

Use property 2 of the radicals to simplify the following. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 55

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 56

Simplify the radical expression as much as possible.

A)
B)
C)
D)
E)

Question 57

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

A)
B)
C)
D)
E)

Question 58

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

A)
B)
C)
D)
E)

Question 59

Simplify the radical expression as much as possible.

A)
B)
C)
D)
E)

Question 60

Use property 2 of the radicals to simplify the following.

A)
B)
C)
D)
E)

Question 61

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

Question 62

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

Question 63

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 64

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 65

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 66

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

Question 67

Simplify the radical expression as much as possible. Assume the variable represents a positive number.

Question 68

Simplify the radical expression as much as possible. Assume all variables represent positive numbers.

Question 69

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 70

Simplify the radical expression as much as possible.

Question 71

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 72

Use property 2 of the radicals to simplify the following.

Question 73

Simplify the radical expression as much as possible. Assume all variables represent positive numbers.

Question 74

Use property 2 of the radicals to simplify the following.

Question 75

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

Question 76

Use combinations of properties 1 and 2 for radicals to simplify the following expression as much as possible. Assume all variables represent positive numbers.

Question 77

Use property 2 of the radicals to simplify the following. Assume all variables represent positive numbers.

Question 78

Simplify the following radical expression as much as possible. Assume the variable represents a positive number.

Question 79

Put the radical expression into simplified form.

A)
B)
C)
D)
E)

Question 80

Simplify the radical expression as much as possible.