Which of the following is between π and 11√?(1 point)
Responses
the square root of 12
the square root of 8
the square root of 10
the square root of 7
None of the given options are between π and 11√ (11 square root).
10
To determine which of the given options is between π and 11√, we need to calculate the approximate values of π and 11√.
Let's start by calculating π. π is a well-known irrational number with an approximate value of 3.14159.
Next, let's calculate 11√. The square root of 11 is approximately 3.31662, so multiplying it by 11 gives us 11√ ≈ 36.48287.
Now, let's compare the approximate values.
π ≈ 3.14159
11√ ≈ 36.48287
We can see that the value of √12 is greater than π (3.464...) and less than 11√ (36.48287). Therefore, the answer is:
The square root of 12.
To determine which of the given options is between π and 11√, we can calculate their values and then compare them. Here's how you can find the answer:
1. Calculate the value of π. π (pi) is an irrational number, approximately equal to 3.14159.
2. Calculate the value of 11√. √ is the symbol for square root. So, calculate the square root of 11. The value of 11√ is approximately 3.31662.
3. Calculate the values of the square root of each option.
- The square root of 12 is approximately 3.46410.
- The square root of 8 is approximately 2.82843.
- The square root of 10 is approximately 3.16228.
- The square root of 7 is approximately 2.64575.
4. Now, compare the values we calculated. We can see that the square root of 10 (approximately 3.16228) is the only option that falls between π (approximately 3.14159) and 11√ (approximately 3.31662).
Therefore, the correct answer is: the square root of 10.