What is the largest integer whose square root is an irrational number between 3 and 4? please.
I think the answer is 15, is that correct?
To find the largest integer whose square root is an irrational number between 3 and 4, we need to find the largest square of an integer that is less than 16 (the square of 4).
Let's start by checking the square of the largest integer less than 4, which is 3. When we square 3, we get 9, which is less than 16. So, the largest integer whose square root is an irrational number between 3 and 4 is 9.
No, that's not correct.
Apologies for the incorrect response. Let's reconsider the problem.
The largest integer whose square root is an irrational number between 3 and 4 can be found by squaring both 3 and 4 to determine their respective square roots and then selecting the largest integer below 4.
The square root of 3 is approximately 1.732, and the square root of 4 is exactly 2. Since we are looking for an irrational number between these values, we should focus on the square root of 3.
The largest integer smaller than 4 whose square root is an irrational number between 3 and 4 is 3.
Yes, you are correct. I apologize for the confusion. The largest integer whose square root is an irrational number between 3 and 4 is indeed 15. The square root of 15 is approximately 3.873, which lies between 3 and 4. Well done!
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. Is the Answer 2 1/8?
To find a rational number between 2 and 214 using the method of adding the numbers together and dividing by 2, we can proceed as follows:
First, add 2 and 214 together: 2 + 214 = 216.
Next, divide the sum by 2: 216 ÷ 2 = 108.
Therefore, the rational number between 2 and 214 using the method described is 108.
However, the answer you have provided, 2 1/8, is not correct. 2 1/8 is a mixed number, and it is not between 2 and 214.
But the answer is exposed to be mixed number.
Apologies for the confusion. Let's proceed with the method you mentioned, adding the numbers together and dividing by 2.
Given: 2 and 214
Summing the numbers: 2 + 214 = 216
Dividing the sum by 2: 216 ÷ 2 = 108
So, the rational number between 2 and 214 obtained using this method is exactly 108, which is not a mixed number. Thus, the answer is 108.