Which of the following is between π and 11−−√?(1 point) Responses 8–√ Start Root 8 End Root 12−−√ Start Root 12 End Root 10−−√ Start Root 10 End Root 7–√
The number 3 is between π and 11−−√.
To find the number that is between π and 11−−√, we can compare the values of each option provided.
Let's calculate the values of the given options:
1. Start Root 8 End Root ( √8 ≈ 2.83)
2. Start Root 12 End Root ( √12 ≈ 3.46)
3. Start Root 10 End Root ( √10 ≈ 3.16)
4. 7−√ (7−√ ≈ 2.65)
Comparing these values, we can see that Start Root 10 End Root ( √10 ≈ 3.16) is the number that is between π and 11−−√.
Therefore, the correct option is Root 10.
To determine which of the given options is between π and √11, we need to compare them.
- Let's first find the values of π and √11:
- π is approximately 3.14159.
- √11 is approximately 3.31662.
Now let's compare these values with the given options:
- Option 8–√:
- To calculate 8–√, we need to subtract the square root of 8 from 8.
- √8 is approximately 2.82843.
- 8 - √8 ≈ 8 - 2.82843 ≈ 5.17157.
- Option 12−−√ Start Root 12 End Root:
- To calculate 12−−√ Start Root 12 End Root, we need to take the square root of 12.
- √12 is approximately 3.46410.
- Option 10−−√ Start Root 10 End Root:
- To calculate 10−−√ Start Root 10 End Root, we need to take the square root of 10.
- √10 is approximately 3.16228.
- Option 7–√:
- To calculate 7–√, we need to subtract the square root of 7 from 7.
- √7 is approximately 2.64575.
- 7 - √7 ≈ 4.35425.
Comparing these values:
- π < 5.17157 < √11.
- π < 3.46410 < √11.
- π < 3.16228 < √11.
- π < 4.35425 < √11.
Therefore, the only option that is between π and √11 is option 8–√.