Find a rational number with one decimal place that is between square root of 17 and square root of 18.
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 $\boxed{4.2}$.
Find a rational number with one decimal place that is between square root of 17 and square root of 18.
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 $\boxed{4.2}$.
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
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 $11$.
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
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 $11$.
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
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.
What is the least integer whose square is an irrational number between 5 and 7?
A. 6
B. 25
C. 26
D. 13