Question
Find a rational number with one decimal place that is between square root of 17 and square root of 18.
Answers
Answered by
GPT 3.5
To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can average the two values. Since $\sqrt{17} \approx 4.123$ and $\sqrt{18} \approx 4.243$, their average is approximately $\frac{4.123+4.243}{2} = \frac{8.366}{2} = 4.183$. Converting this to a rational number with one decimal place, we have $\boxed{4.2}$.
Answer
Find a rational number with one decimal place that is between square root of 17 and square root of 18.
Answered by
GPT 3.5
To find a rational number between $\sqrt{17}$ and $\sqrt{18}$, we can use the fact that the average of two numbers lies between them.
The square root of 17 is between 4 and 5, while the square root of 18 is between 4 and 5.5.
Therefore, a rational number with one decimal place that lies between $\sqrt{17}$ and $\sqrt{18}$ is $\boxed{4.2}$.
The square root of 17 is between 4 and 5, while the square root of 18 is between 4 and 5.5.
Therefore, a rational number with one decimal place that lies between $\sqrt{17}$ and $\sqrt{18}$ is $\boxed{4.2}$.
Answer
Which of the following is between t and 11? (1 point)
A. Square root of 8
B. Square root of 10
C. Square root of 7
D. Square root of 12
A. Square root of 8
B. Square root of 10
C. Square root of 7
D. Square root of 12
Answered by
GPT 3.5
To determine which of the given options is between $t$ and $11$, we need to compare the values of each option.
Since we do not have any information about $t$, we cannot make a specific comparison with it. However, we can compare the values of each option with $11$ to see which lies between them.
Calculating, we find:
- The square root of $8$ is approximately $2.83$.
- The square root of $10$ is approximately $3.16$.
- The square root of $7$ is approximately $2.65$.
- The square root of $12$ is approximately $3.46$.
From the given options, only $\boxed{\text{B. Square root of 10}}$ lies between $t$ and $11$, as $3.16$ is greater than $t$ and less than $11$.
Since we do not have any information about $t$, we cannot make a specific comparison with it. However, we can compare the values of each option with $11$ to see which lies between them.
Calculating, we find:
- The square root of $8$ is approximately $2.83$.
- The square root of $10$ is approximately $3.16$.
- The square root of $7$ is approximately $2.65$.
- The square root of $12$ is approximately $3.46$.
From the given options, only $\boxed{\text{B. Square root of 10}}$ lies between $t$ and $11$, as $3.16$ is greater than $t$ and less than $11$.
Answer
Which of the following is between pi and 11? (1 point)
A. Square root of 8
B. Square root of 10
C. Square root of 7
D. Square root of 12
A. Square root of 8
B. Square root of 10
C. Square root of 7
D. Square root of 12
Answered by
GPT 3.5
To determine which of the given options is between $\pi$ and $11$, we need to compare the values of each option.
Since $\pi \approx 3.14$ and $11 > 3.14$, any option that results in a value greater than $\pi$ and less than $11$ will be our answer.
Calculating, we find:
- The square root of $8$ is approximately $2.83$.
- The square root of $10$ is approximately $3.16$.
- The square root of $7$ is approximately $2.65$.
- The square root of $12$ is approximately $3.46$.
From the given options, only $\boxed{\text{B. Square root of 10}}$ lies between $\pi$ and $11$, as $3.16$ is greater than $\pi$ and less than $11$.
Since $\pi \approx 3.14$ and $11 > 3.14$, any option that results in a value greater than $\pi$ and less than $11$ will be our answer.
Calculating, we find:
- The square root of $8$ is approximately $2.83$.
- The square root of $10$ is approximately $3.16$.
- The square root of $7$ is approximately $2.65$.
- The square root of $12$ is approximately $3.46$.
From the given options, only $\boxed{\text{B. Square root of 10}}$ lies between $\pi$ and $11$, as $3.16$ is greater than $\pi$ and less than $11$.
Answer
Show an example of an irrational number between 9 and 11.
A. Square root of 100
B. Square root of 20
C. Square root of 10
D. Square root of 99
A. Square root of 100
B. Square root of 20
C. Square root of 10
D. Square root of 99
Answered by
GPT 3.5
To determine an irrational number between 9 and 11, we need to find a value that is greater than 9 and less than 11, but that is not a perfect square.
Calculating, we find:
- The square root of 100 is 10, which is not between 9 and 11.
- The square root of 20 is approximately 4.47, which is not between 9 and 11.
- The square root of 10 is approximately 3.16, which is not between 9 and 11.
- The square root of 99 is approximately 9.95, which is between 9 and 11.
From the given options, $\boxed{\text{D. Square root of 99}}$ is an example of an irrational number between 9 and 11.
Calculating, we find:
- The square root of 100 is 10, which is not between 9 and 11.
- The square root of 20 is approximately 4.47, which is not between 9 and 11.
- The square root of 10 is approximately 3.16, which is not between 9 and 11.
- The square root of 99 is approximately 9.95, which is between 9 and 11.
From the given options, $\boxed{\text{D. Square root of 99}}$ is an example of an irrational number between 9 and 11.
Answer
What is the least integer whose square is an irrational number between 5 and 7?
A. 6
B. 25
C. 26
D. 13
A. 6
B. 25
C. 26
D. 13
Answered by
GPT 3.5
To find the least integer whose square is an irrational number between 5 and 7, we need to determine the integer whose square lies between the square roots of 5 and 7.
Calculating, we find:
- The square root of 5 is approximately 2.24. The square of 2 is 4, which is not between 5 and 7.
- The square root of 7 is approximately 2.65. The square of 3 is 9, which is not between 5 and 7.
Therefore, there is no integer whose square lies between the square roots of 5 and 7. Thus, the answer is $\boxed{\text{None of the above}}$.
Calculating, we find:
- The square root of 5 is approximately 2.24. The square of 2 is 4, which is not between 5 and 7.
- The square root of 7 is approximately 2.65. The square of 3 is 9, which is not between 5 and 7.
Therefore, there is no integer whose square lies between the square roots of 5 and 7. Thus, the answer is $\boxed{\text{None of the above}}$.
Answer
Show am example of a rational number that is between square root of 10 and square root of 11.
A. 16/5
B. 3.1
C. 3.4
D. 10/3
A. 16/5
B. 3.1
C. 3.4
D. 10/3
Answered by
GPT 3.5
To find a rational number between $\sqrt{10}$ and $\sqrt{11}$, we can look for a rational number whose square lies between $10$ and $11$.
Calculating, we find:
- $\left(\frac{16}{5}\right)^2 = \frac{256}{25} = 10.24$, which is not between $10$ and $11$.
- $3.1^2 = 9.61$, which is not between $10$ and $11$.
- $3.4^2 = 11.56$, which is not between $10$ and $11$.
- $\left(\frac{10}{3}\right)^2 = \frac{100}{9} = 11.\overline{1}$, which is not between $10$ and $11$.
From the given options, none of them produce a rational number between $\sqrt{10}$ and $\sqrt{11}$. Thus, the answer is $\boxed{\text{None of the above}}$.
Calculating, we find:
- $\left(\frac{16}{5}\right)^2 = \frac{256}{25} = 10.24$, which is not between $10$ and $11$.
- $3.1^2 = 9.61$, which is not between $10$ and $11$.
- $3.4^2 = 11.56$, which is not between $10$ and $11$.
- $\left(\frac{10}{3}\right)^2 = \frac{100}{9} = 11.\overline{1}$, which is not between $10$ and $11$.
From the given options, none of them produce a rational number between $\sqrt{10}$ and $\sqrt{11}$. Thus, the answer is $\boxed{\text{None of the above}}$.