Which of the following is between π and 11−−√?(1 point)
√10
√8
√12
√7
√10 is between π and 11−−√.
Find a rational number between 2 and 214
using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we can calculate:
(2 + 214) / 2 = 216 / 2 = 108
So, the rational number between 2 and 214 is 108. Since it is a whole number, it can be written as a mixed number as follows:
108 = 108/1 = 108 0/1
Therefore, the answer as a mixed number is 108 0/1.
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
To find the largest integer whose square root is an irrational number between 3 and 4, we need to find the largest perfect square (integer squared) between 9 and 16.
The perfect squares between 9 and 16 are 9 and 16.
The square root of 9 is 3, which is not an irrational number as it is an integer.
The square root of 16 is 4, which is also not an irrational number as it is an integer.
Since there are no perfect squares whose square roots are irrational numbers between 3 and 4, there is no largest integer with this property.
thats not right
Apologies for the incorrect response. Let's try solving the problem again.
The largest integer whose square root is an irrational number between 3 and 4 can be found by finding the square of the largest integer between the square roots of the given numbers.
The square root of 3 is approximately 1.732, and the square root of 4 is exactly 2.
Thus, the largest integer between 1.732 and 2 is 1.
The square root of 1 is 1, which is an irrational number between 3 and 4.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 1.
Find a rational number between 2 and 214
using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we can calculate:
(2 + 214) / 2 = 216 / 2 = 108
So, the rational number between 2 and 214 is 108. Since it is a whole number, it can be written as a mixed number as follows:
108 = 108/1 = 108 0/1
Therefore, the answer as a mixed number is 108 0/1.
To determine which of the given options is between π and 11−√, we can evaluate each option and compare them to π and 11−√.
Let's start by finding the values of π and 11−√:
- The value of π (pi) is approximately 3.14159.
- To find 11−√, we need to subtract the square root of 8 (2√2) from 11, which gives us approximately 11 - 2√2 ≈ 11 - 2 * 1.414 ≈ 11 - 2.828 ≈ 8.172.
Now, let's evaluate the given options:
1. √10 ≈ 3.162
2. √8 ≈ 2.828
3. √12 ≈ 3.464
4. √7 ≈ 2.646
Comparing the options to π and 11−√:
π < √10 < 11−√ < √8 < √12 < √7
From the comparison, we can see that √10 is between π and 11−√.
Therefore, the answer is √10.