AnswersFL-1200700-Mathematics for College Algebra MISEstimating and Comparing Square Roots

Estimating and Comparing Square Roots Answers

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1
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The point is plotted on the number line. What whole number best approximates the value of x?

Question illustration
A
100
B
102
C
103
D
104
2
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Jana is ordering a list of numbers from least to greatest.Which statement can be used to create her list?

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A
is less than because and the square root of a number less than 1 is less than the number itself.
Option A
B
is greater than because and the square root of a number greater than 1 is greater than the number itself.
Option B
C
is less than because and is between 6 and 8.
Option C
D
is greater than because is less than 1 and the square root of a number greater than 1 is greater than 1.
Option D
3

Hassan used the iterative process to locate on the number line. Which best describes Hassan’s estimation?

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A
Hassan is correct because
Option A
B
Hassan is correct because the point is on the middle of the number line.
C
Hassan is incorrect because is less than 0.4.
Option C
D
Hassan is incorrect because the point should be located between 0.1 and 0.2.
4

Which is the best estimate of to the nearest tenth?

Question illustration
A
6.8
B
6.9
C
7.0
D
7.1
5

Which inequalities are true? Select the four correct answers.

A
StartRoot 5 EndRoot less-than 2.3 less-than StartRoot 6 EndRoot
Option A
B
StartRoot 5 EndRoot less-than 2.4 less-than StartRoot 6 EndRoot
Option B
C
StartRoot 4 EndRoot less-than StartRoot 5 EndRoot less-than StartRoot 5.5 EndRoot
Option C
D
StartRoot 8 EndRoot less-than 3 less-than StartRoot 9 EndRoot
Option D
E
StartRoot 8 EndRoot less-than 2.9 less-than StartRoot 9 EndRoot
Option E
F
StartRoot 4 EndRoot less-than 4.5 less-than StartRoot 5 EndRoot
Option F
6

Which statements are true? Select the five correct answers.

A
< 1.8
Option A
B
StartRoot 1.8 EndRoot greater-than 1
Option B
C
StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
Option C
D
1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
Option D
E
StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
Option E
F
StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
Option F
7

The values and are plotted on the number line.What is the approximate difference in tenths between and ?

Question illustration
A
0.3
B
0.7
C
1.3
D
2.2
8

Four students provide the following approximations for .Anyah states that is between 0.44 and 0.45 because .Matthew states that is between 0 and 1 because .Rhoda states that is between 0.9 and 1.0 because .Ming states that is between 0.93 and 0.95 because .Which solution(s) are correct?

Question illustration
A
Anyah's only
B
Ming's only
C
Anyah’s, Matthew’s, and Rhoda’s
D
Matthew’s, Rhoda’s, and Ming’s
9

Which two numbers does lie between on a number line?

Question illustration
A
7.7 and 7.8
B
7.8 and 7.9
C
7.9 and 8.0
D
8.0 and 8.1
10

Nolan used the following procedure to find an estimate for .Step 1: Since and and 16 < 18 < 25, is between 4 and 5.Step 2: Since 18 is closer to 16, square the tenths closer to 4.Step 3: Since 18.49 rounds to 18, 4.3 is the best approximation for .In which step, if any, did Nolan make an error?

Question illustration
A
In step 1, is between 4 and 5 because 20 and .
Option A
B
In step 2, he made a calculation error when squaring.
C
In step 3, he should have determined which square is closest to 18.
D
Nolan did not make an error.
11

Which point best approximates ?

Question illustration
A
A
B
B
C
C
D
D
12

Which point best approximates?

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A
A
B
B
C
C
D
D
13

The point plotted on the number line is .What is the approximate value of x?

Question illustration
A
4
B
9
C
17
D
20
14

What square root best approximates the point on the graph?

Question illustration
A
StartRoot 5 EndRoot
Option A
B
StartRoot 15 EndRoot
Option B
C
StartRoot 28 EndRoot
Option C
D
StartRoot 53 EndRoot
Option D
15

Which statements are true? Select the two correct answers.

A
The square root of a positive number greater than 1 is less than the number.
B
The square root of a positive number is always less than half of the number itself.
C
The square root of a positive number less than 1 is less than the number.
D
The square root of a perfect square is not a whole number.
E
The square root of a positive number less than 1 is between 0 and 1.
16

Which two numbers does lie between on a number line?

Question illustration
A
7.0 and 7.1
B
7.1 and 7.2
C
7.2 and 7.3
D
7.3 and 7.4
17

Which number is farthest from 2 on the number line?

A
StartRoot 2.1 EndRoot
Option A
B
StartRoot 2.4 EndRoot
Option B
C
StartRoot 2.5 EndRoot
Option C
D
StartRoot 2.9 EndRoot
Option D
18

Which two numbers does lie between on a number line?

Question illustration
A
11.0 and 11.1
B
11.2 and 11.3
C
11.3 and 11.4
D
11.4 and 11.5

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