Which of the following is between π and 11−−√?
10−−√
Since $\sqrt{11}>3$ (since $3^2=9<11$, but $4^2=16>11$), we have $11-\sqrt{11}<11-3=8$. Since $\pi$ is between 3 and 4 (since $3.14=\pi<3.15$), we have $3<\pi<4$. Putting it all together, we have $$\pi<4<11-\sqrt{11}<8.$$Therefore, $\boxed{4}$ is between $\pi$ and $11-\sqrt{11}$.
Which of the following is between π and 11−−√?(1 point)
Responses
10−−√
Start Root 10 End Root
12−−√
Start Root 12 End Root
7–√
Start Root 7 End Root
8–√
To determine which number is between π and 11−−√, we can compare their values.
The value of π is approximately 3.14159.
To find the value of 11−−√, we need to take the square root of 11. The square root of 11 is approximately 3.31662.
Comparing the values, we can see that 3.31662 is between 3.14159 and 11. Therefore, 11−−√ is the number that is between π and 11−−√.
To determine which number is between π and 11−−√, we need to compare the values of π and 11−−√.
π is a constant representing the mathematical value of pi, which is approximately 3.14159.
On the other hand, to find the value of 11−−√, we need to calculate the square root of 11.
Using the square root function, we find that the square root of 11 is approximately 3.31662.
So, π is approximately 3.14159 and 11−−√ is approximately 3.31662.
Comparing the two values, we can see that the number between π and 11−−√ is approximately 3.142.