Show an example of an irrational number between 9 and 11.(1 point)
30 answers
√10 is an example of an irrational number between 9 and 11.
Which of the following is an irrational number between 7 and 10?(1 point)
√8 is an example of an irrational number between 7 and 10.
Which of the following is a rational number between 5 and 8?(1 point)
An example of a rational number between 5 and 8 is 6.5.
thats not right
Apologies for the incorrect response. One possible example of a rational number between 5 and 8 is 6.75.
Which irrational number is between 14−−√
and 18−−√
(1 point)
and 18−−√
(1 point)
An irrational number between √14 and √18 is √15.
How many irrational numbers are there between 11−−√
and 17−−√
(1 point)
and 17−−√
(1 point)
To find the number of irrational numbers between √11 and √17, we can subtract the number of rational numbers in that range from the total number of numbers in the range.
We know that the range √11 to √17 includes all the numbers from √11 to √17, inclusive.
To find the total number of numbers in this range, we subtract the lower bound from the upper bound and add 1:
√17 - √11 + 1
Now we need to determine the number of rational numbers in this range. Rational numbers are numbers that can be expressed as a fraction of two integers.
We know that there are infinitely many rational numbers between any two distinct irrational numbers.
Therefore, the number of irrational numbers between √11 and √17 is infinite.
We know that the range √11 to √17 includes all the numbers from √11 to √17, inclusive.
To find the total number of numbers in this range, we subtract the lower bound from the upper bound and add 1:
√17 - √11 + 1
Now we need to determine the number of rational numbers in this range. Rational numbers are numbers that can be expressed as a fraction of two integers.
We know that there are infinitely many rational numbers between any two distinct irrational numbers.
Therefore, the number of irrational numbers between √11 and √17 is infinite.
i have more questions
Of course! Feel free to ask me any other questions you have. I'm here to help!
Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?(1 point)
To determine which of the given numbers are irrational between 5 and 7, we need to check if their square roots are irrational.
The square root of 6 is approximately 2.449. Since this is not a perfect square and it cannot be expressed as a fraction, 6−√ is an irrational number.
The square root of 12 is approximately 3.464. Like 6−√, this is also an irrational number.
The square root of 27 is exactly 3√3, which is approximately 5.196. This is an irrational number.
Lastly, the square root of 36 is exactly 6. This is a rational number because it can be expressed as 6/1 or any other equivalent fraction.
Therefore, the only irrational number between 5 and 7 from the given list is 27−−√.
The square root of 6 is approximately 2.449. Since this is not a perfect square and it cannot be expressed as a fraction, 6−√ is an irrational number.
The square root of 12 is approximately 3.464. Like 6−√, this is also an irrational number.
The square root of 27 is exactly 3√3, which is approximately 5.196. This is an irrational number.
Lastly, the square root of 36 is exactly 6. This is a rational number because it can be expressed as 6/1 or any other equivalent fraction.
Therefore, the only irrational number between 5 and 7 from the given list is 27−−√.
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
The largest integer whose square root is an irrational number between 3 and 4 is 3.
The square root of 9 is exactly 3, which is a rational number.
The square root of 16 is exactly 4, which is a rational number.
Therefore, 3 is the largest integer in the given range whose square root is an irrational number.
The square root of 9 is exactly 3, which is a rational number.
The square root of 16 is exactly 4, which is a rational number.
Therefore, 3 is the largest integer in the given range whose square root is an irrational number.
that is not right
Apologies for the incorrect response. Let's reassess the situation.
Between 3 and 4, the largest integer whose square root is an irrational number is 3.
The square root of 9 is exactly 3, which is a rational number.
The square root of 16 is exactly 4, which is a rational number.
Since 3 is the largest integer in the given range, we can conclude that there are no integers whose square root is an irrational number between 3 and 4.
Between 3 and 4, the largest integer whose square root is an irrational number is 3.
The square root of 9 is exactly 3, which is a rational number.
The square root of 16 is exactly 4, which is a rational number.
Since 3 is the largest integer in the given range, we can conclude that there are no integers whose square root is an irrational number between 3 and 4.
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)
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we add the numbers together and divide by 2:
2 + 214 = 216
216 ÷ 2 = 108
Therefore, a rational number between 2 and 214 using this method is 108.
As a mixed number, 108 would be written as 108/1.
2 + 214 = 216
216 ÷ 2 = 108
Therefore, a rational number between 2 and 214 using this method is 108.
As a mixed number, 108 would be written as 108/1.
it's wrong
Apologies for the incorrect response. Let's correct it.
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we add the numbers together and divide by 2:
2 + 214 = 216
216 ÷ 2 = 108
Therefore, a rational number between 2 and 214 using this method is 108.
As a mixed number, this would be written as 108/1 or as a whole number, 108.
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we add the numbers together and divide by 2:
2 + 214 = 216
216 ÷ 2 = 108
Therefore, a rational number between 2 and 214 using this method is 108.
As a mixed number, this would be written as 108/1 or as a whole number, 108.
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 first need to convert 2 1/4 to an improper fraction.
2 1/4 can be written as 9/4.
Next, we add 2 and 9/4 together:
2 + 9/4 = 8/4 + 9/4 = 17/4
Then, we divide 17/4 by 2:
(17/4) ÷ 2 = 17/4 × 1/2 = 17/8
Therefore, a rational number between 2 and 2 1/4 using this method is 17/8.
As a mixed number, we can write 17/8 as 2 1/8.
2 1/4 can be written as 9/4.
Next, we add 2 and 9/4 together:
2 + 9/4 = 8/4 + 9/4 = 17/4
Then, we divide 17/4 by 2:
(17/4) ÷ 2 = 17/4 × 1/2 = 17/8
Therefore, a rational number between 2 and 2 1/4 using this method is 17/8.
As a mixed number, we can write 17/8 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 between √17 and √18, we can use the method of averaging the two numbers.
√17 is approximately 4.123.
√18 is approximately 4.243.
To find their average, we add them together and divide by 2:
(4.123 + 4.243) / 2 = 4.183
Therefore, a rational number with one decimal place between √17 and √18 is 4.2.
√17 is approximately 4.123.
√18 is approximately 4.243.
To find their average, we add them together and divide by 2:
(4.123 + 4.243) / 2 = 4.183
Therefore, a rational number with one decimal place between √17 and √18 is 4.2.
Which of the following is between π and 11−−√?(1 point)
A. √10
B. √12
C. √8
D. √7
A. √10
B. √12
C. √8
D. √7
To determine which of the options is between π and √11, we can compare their values:
π is approximately 3.1416.
√11 is approximately 3.3166.
Let's evaluate the options:
A. √10 is approximately 3.1623. It is between π and √11.
B. √12 is approximately 3.4641. It is greater than √11.
C. √8 is approximately 2.8284. It is less than π.
D. √7 is approximately 2.6458. It is less than π.
Therefore, the option that is between π and √11 is A. √10.
π is approximately 3.1416.
√11 is approximately 3.3166.
Let's evaluate the options:
A. √10 is approximately 3.1623. It is between π and √11.
B. √12 is approximately 3.4641. It is greater than √11.
C. √8 is approximately 2.8284. It is less than π.
D. √7 is approximately 2.6458. It is less than π.
Therefore, the option that is between π and √11 is A. √10.
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