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Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 9

Real Numbers and Right Triangles

Educators


Problem 1

Find each square root.
$$
\sqrt{25}
$$

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Problem 2

Find each square root.
$$-\sqrt{64}$$

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Problem 3

Find each square root
$\pm \sqrt{81}$

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Problem 4

Find each square root.
$\sqrt{25}$

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Problem 5

Use a calculator to find each square root to the nearest tenth.
$-\sqrt{32}$

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Problem 6

Estimate each square root to the nearest integer. Do not use a calculator.
$$\sqrt{66}$$

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Problem 7

Estimate each square root to the nearest integer. Do not use a calculator.
$$-\sqrt{103}$$

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Problem 8

A baseball diamond is actually a square with an area of 8100 square feet. The Cincinnati Reds cover their diamond with a tarp to protect it from the rain. The sides are all the same length. How long is the tarp on each side?

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Problem 9

Find each square root.
$$\sqrt{16}$$

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Problem 10

Find each square root.
$$\sqrt{49}$$

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Problem 11

Find each square root.
$$-\sqrt{1}$$

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Problem 12

Find each square root.
$$-\sqrt{25}$$

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Problem 13

Find each square root.
$$\pm \sqrt{100}$$

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Problem 14

Find each square root.
$$\pm \sqrt{196}$$

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Problem 15

Use a calculator to find each square root to the nearest tenth.
$$\sqrt{30}$$

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Problem 16

Use a calculator to find each square root to the nearest tenth.
$$\sqrt{56}$$

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Problem 17

Use a calculator to find each square root to the nearest tenth.
$$-\sqrt{43}$$

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Problem 18

Use a calculator to find each square root to the nearest tenth.
$$-\sqrt{86}$$

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Problem 19

Use a calculator to find each square root to the nearest tenth.
$$\sqrt{180}$$

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Problem 20

Use a calculator to find each square root to the nearest tenth.
$$\sqrt{250}$$

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Problem 21

Use a calculator to find each square root to the nearest tenth.
$$\pm \sqrt{0.75}$$

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Problem 22

Use a calculator to find each square root to the nearest tenth.
$$\pm \sqrt{3.05}$$

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Problem 23

Estimate each square root to the nearest integer. Do not use a calculator.
$$\sqrt{79}$$

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Problem 24

Estimate each square root to the nearest integer. Do not use a calculator.
$$\sqrt{95}$$

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Problem 25

Estimate each square root to the nearest integer. Do not use a calculator.
$$
-\sqrt{54}
$$

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Numerade Educator

Problem 26

Estimate each square root to the nearest integer. Do not use a calculator.
$$-\sqrt{125}$$

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Problem 27

Estimate each square root to the nearest integer. Do not use a calculator.
$$\pm \sqrt{200}$$

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Problem 28

Estimate each square root to the nearest integer. Do not use a calculator.
$$\pm \sqrt{396}$$

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Problem 29

Use the table shown and refer to Example 4 on page 466.
(TABLE CAN NOT COPY)
On a clear day, estimate how far a person can see from the top hill of the Vortex. Then calculate the distance.

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Problem 30

Use the table shown and refer to Example 4 on page 466.
(TABLE CAN NOT COPY)
Estimate how far a person can see on a clear day from the top hill of the Titan. Then calculate the distance.

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Problem 31

Use the Internet or another source to find the tallest roller coaster in the world. How far would you be able to see from the top of the roller coaster on a clear day?

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Problem 32

The number $\sqrt{54}$ lies between which two consecutive whole numbers?

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Problem 33

Which is greater, $\sqrt{65}$ or $9 ?$ Explain your reasoning.

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Problem 34

Which is less, 11 or $\sqrt{120} ?$ Explain your reasoning.

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Problem 35

Find a square root that lies between 17 and 18 .

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Problem 36

Order $\sqrt{77},-8,-\sqrt{83}, 9,-10,-\sqrt{76}, \sqrt{65}$ from least to greatest.

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Problem 37

The area of each square is given. Estimate the length of a side of each square to the nearest tenth. Then find its approximate perimeter.
(FIGURE CAN NOT COPY)

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Problem 38

The area of each square is given. Estimate the length of a side of each square to the nearest tenth. Then find its approximate perimeter.
(FIGURE CAN NOT COPY)

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Problem 39

The area of each square is given. Estimate the length of a side of each square to the nearest tenth. Then find its approximate perimeter.
(FIGURE CAN NOT COPY)

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Problem 40

Find the negative square root of 1000 to the nearest tenth.

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Problem 41

If $x=\sqrt{5000},$ what is the value of $x$ to the nearest tenth?

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Problem 42

City code requires that a reception hall must allow 4 square feet for each person on the dance floor. The reception hall wants to have a dance floor that is a square and that is large enough for 100 people at a time. What is the length of each side of the dance floor?

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Problem 43

Estimate the perimeter of a square that has an area of 2080 square meters. Then calculate the perimeter. Round to the nearest tenth.

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Problem 44

Write a number for which the negative square root is not an integer. Then graph the negative square root.

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Problem 45

What are the possibilities for the ending digit of a number that has a whole number square root? Explain your reasoning.

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Problem 46

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation.
Use inverse operations to evaluate each expression.
$$(\sqrt{64})^{2}$$

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Problem 47

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation.
Use inverse operations to evaluate each expression.
$$(\sqrt{100})^{2}$$

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Problem 48

Use the following information. Squaring a number and finding the square root of a number are inverse operations. That is, one operation undoes the other operation.
Use inverse operations to evaluate each expression.
$$(\sqrt{169})^{2}$$

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Problem 49

Use the pattern from Exercises $46-48$ to find $(\sqrt{a})^{2}$ if $a \geq 0$.

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Problem 50

How are square roots related to factors? Give an example of a number between 100 and 200 whose square root is a whole number and an example of a number between 100 and 200 whose square root is a decimal that does not terminate.

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Problem 51

Which point on the number line best represents $\sqrt{210 ?}$
(FIGURE CAN NOT COPY)
$$\begin{array}{llll}
\text { A } A & \text { B } B & \text { C } C & \text { D } D
\end{array}$$

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Problem 52

The area of each square is 25 square units. Find the perimeter of the figure.
(FIGURE CAN NOT COPY)
F 60 units
H 100 units
G 75 units
J 125 units

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Problem 53

Solve each inequality.
$$4 y>24$$

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Problem 54

Solve each inequality.
$$\frac{a}{0.3}<-7$$

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Problem 55

Solve each inequality.
$$18 \geq-2 k$$

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Problem 56

Solve each inequality.
$$2 x+5<17$$

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Problem 57

Solve each inequality.
$$2 t-3 \geq 1.4 t+6$$

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Problem 58

Solve each inequality.
$$12 r-4>7+12 r$$

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Problem 59

Ice cream sales increase as the temperature outside increases. Describe the slope of a line of fit that represents this situation.

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Problem 60

Determine whether the relation $(4,-1),(3,5),(-4,1),(4,2)$ is a function.

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Problem 61

Martin drives 6 hours at an average rate of 65 miles per hour. What is the distance Martin travels? Use $d=r t$.

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Problem 62

Explain why each number is a rational number.
$$\frac{10}{2}$$

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Problem 63

Explain why each number is a rational number.
$$1 \frac{1}{2}$$

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Problem 64

Explain why each number is a rational number.
$$0.75$$

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Problem 65

Explain why each number is a rational number.
$$0 . \overline{8}$$

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Problem 66

Explain why each number is a rational number.
$$6$$

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Problem 67

Explain why each number is a rational number.
$$-7$$

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