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, we must first find the sum of 2 and 2 1/4:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4.
Now, divide 17/4 by 2:
(17/4) / 2 = 17/4 ÷ 2 = 17/4 × 1/2 = 17/8.
Thus, a rational number between 2 and 2 1/4 using the given method is 17/8.
Writing 17/8 as a mixed number, we convert it to a mixed fraction:
17 ÷ 8 = 2 remainder 1.
Thus, 17/8 as a mixed number is 2 1/8.
To find a rational number with one decimal place between √17 and √18, we can use the method of averaging.
First, find the average of √17 and √18:
(√17 + √18) / 2
Now find the square root of 17 and 18:
√17 ≈ 4.123
√18 ≈ 4.243
Taking the average:
(4.123 + 4.243) / 2 ≈ 4.183
Thus, a rational number with one decimal place between √17 and √18 is approximately 4.2.
To determine which of the given options is between π and √11, we can compare the values.
π is approximately 3.14, and √11 is approximately 3.32.
Let's examine each option:
- √12 is approximately 3.464. This is larger than both π and √11, so it is not between them.
- √8 is approximately 2.828. This is smaller than both π and √11, so it is not between them.
- √10 is approximately 3.162. This is larger than π, but smaller than √11, so it is between them.
- √7 is approximately 2.646. This is smaller than both π and √11, so it is not between them.
Therefore, the option that is between π and √11 is √10.
Find a rational number with one decimal place that is between √17 and √18.
Which of the following is between π and √11? (1 point)
Responses
√12
√8
√10
√7
Show an example of an irrational number between 9 and 11. (1 point)
Responses
√20
√99
√10
√100
To determine an example of an irrational number between 9 and 11, we can evaluate the given options:
- √20 ≈ 4.472. This is larger than both 9 and 11, so it is not between them.
- √99 ≈ 9.949. This is larger than both 9 and 11, so it is not between them.
- √10 ≈ 3.162. This is smaller than both 9 and 11, so it is not between them.
- √100 = 10. This is larger than both 9 and 11, so it is not between them.
Since none of the given options satisfy the requirement of being between 9 and 11, we need to find a different irrational number within this range.
An example of an irrational number between 9 and 11 is π. Pi, approximately 3.14159, is irrational and falls between 9 and 11.
What is the least integer whose square root is an irrational number between 5 and 7? (1 point)
Responses
13
25
6
26
To determine the least integer whose square root is an irrational number between 5 and 7, we need to evaluate the square roots of the given options:
- √13 ≈ 3.606: This is larger than 3, so it is not between 5 and 7.
- √25 = 5: This is not an irrational number, so it is not between 5 and 7.
- √6 ≈ 2.449: This is smaller than 3, so it is not between 5 and 7.
- √26 ≈ 5.099: This is not an irrational number, so it is not between 5 and 7.
Since none of the given options satisfy the requirement of having an irrational square root between 5 and 7, we need to find a different answer.
The next integer to check is 16. √16 = 4, which is not between 5 and 7.
Next, we check 17. √17 ≈ 4.123, which is between 5 and 7.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 17.