Find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, you need to convert 2 1/4 to an improper fraction.
2 1/4 = (2 * 4 + 1) / 4 = 9/4
Now, add 2 and 9/4 together:
2 + 9/4 = 8/4 + 9/4 = 17/4
Next, divide 17/4 by 2:
(17/4) ÷ 2 = 17/4 ÷ 2/1 = 17/4 * 1/2 = (17*1) / (4*2) = 17/8
Therefore, the rational number between 2 and 2 1/4 using the given method is 17/8.
As a mixed number, this can be written as 2 1/8.
Find a rational number with one decimal place that is between 17−−√ and 18−−√.(1 point)
To find a rational number with one decimal place that is between √17 and √18, we can approximate the square roots as follows:
√17 ≈ 4.123
√18 ≈ 4.243
Now, we can find a rational number between these two approximation by taking their average and rounding to one decimal place:
(4.123 + 4.243) / 2 ≈ 4.183
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
Show an example of an irrational number between 9 and 11.(1 point)
Responses
99−−√
square root of 99
20−−√
square root of 20
10−−√
square root of 10
100−−−√
square root of 100
An example of an irrational number between 9 and 11 is √10 (the square root of 10). The value of √10 is approximately 3.16.
Which of the following is an irrational number between 7 and 10?(1 point)
Responses
To identify an irrational number between 7 and 10, we can check the given options:
- square root of 49
- square root of 64
- square root of 81
- square root of 100
The square root of 49 is 7, which is not an irrational number.
The square root of 64 is 8, which is also not an irrational number.
The square root of 81 is 9, which is still not an irrational number.
The square root of 100 is 10, which is not an irrational number either.
Therefore, none of the given options represents an irrational number between 7 and 10.
Which of the following is an irrational number between 7 and 10?(1 point)
Responses
8–√
square root of 8
55−−√
square root of 55
64−−√
square root of 64
81−−√
To find an irrational number between 7 and 10, we can check the given options:
- √8 (square root of 8)
- √55 (square root of 55)
- √64 (square root of 64)
- √81 (square root of 81)
The square root of 8 is approximately 2.828, which is an irrational number.
The square root of 55 is approximately 7.416, which is also an irrational number.
The square root of 64 is 8, which is not an irrational number.
The square root of 81 is 9, which is not an irrational number.
Therefore, the irrational numbers between 7 and 10 are √8 and √55.
Which of the following is a rational number between 5 and 8?(1 point)
To identify a rational number between 5 and 8, we can check the given options:
- square root of 25
- pi
- 7
- square root of 64
The square root of 25 is 5, which is a rational number.
Pi is an irrational number and not a rational number.
7 is a rational number and falls between 5 and 8.
The square root of 64 is 8, which is a rational number.
Therefore, the rational number between 5 and 8 is 7.
Which of the following is a rational number between 5 and 8?(1 point)
Responses
28−−√
square root of 28
36−−√
square root of 36
40−−√
square root of 40
80−−√
To identify a rational number between 5 and 8, we can check the given options:
- √28 (square root of 28)
- √36 (square root of 36)
- √40 (square root of 40)
- √80 (square root of 80)
The square root of 28 is approximately 5.29, which is not a rational number.
The square root of 36 is 6, which is a rational number.
The square root of 40 is approximately 6.32, which is not a rational number.
The square root of 80 is approximately 8.94, which is not a rational number.
Therefore, the only rational number between 5 and 8 is √36, which is equal to 6.
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
To find the largest integer whose square root is an irrational number between 3 and 4, we need to determine the largest perfect square that is less than 4.
The largest perfect square less than 4 is 3^2 = 9.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 9.
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, you need to add 2 and 214 together and then divide the sum by 2.
2 + 214 = 216
216 ÷ 2 = 108
Therefore, the rational number between 2 and 214 is 108.
As a mixed number, this can be written as 108/1.